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Tonal voice-leading in Schoenberg’s opus 15 McNab, Grace A. L. 1982

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TONAL VOICE-LEADING IN SCHOENBERG'S OPUS 15 Grace A. L. McNab B. Mus., The University of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF MUSIC i n THE FACULTY OF GRADUATE STUDIES Department of Music We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1982 © Grace A. L. McNab, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f Music The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date March 2b, 1 9 8 2 DE-6 (3/81) V i i ABSTRACT This study deals with the processes of tonal counterpoint inherent i n the songs of Schoenberg's Opus 15 i "Book of the Hanging Gardens" and, by implication, i n re l a t e d works. Chapter I, "The Concept of Harmonic Voice", introduces the conceptual key to the manner of investigation presented herein. Simply stated, "harmonic voices" consist of the strongly-directed, predictable motions by semitone and whole-tone, and the common-tone connections which occur from one chord to the next i n a tonal progression. Examples of strongly-directed motions are the r i s i n g of the leading-tone and f a l l i n g of the minor seventh of a dominant-seventh chord, and the diverging motions present when an augmented six t h progresses to an octave on the dominant. To show how the harmonic voice concept may be applied i n analysis, passages from Opus 6, Number k are examined. Chapter II, "Harmonic Procedures Which Minimize Diatonic-Chromatic Differences", deals with s p e c i f i c types of harmonic voice motion which are common to chromatic passages and simpler, more overtly tonal ones. The lack of importance which the harmonic voice concept attributes to the presence or absence of the root of a chord i s emphasized. The harmonic procedures discussed come under the following subject headings: "The Tritone-Substitute", "The Minor-i i i Seventh/Augmented-Sixth Potential of 'Whole-tone' Chords", "Double-Neighbor Pairs i n 'Whole-tone* and Other Contexts", "The Minor-Third Relationship", and "The Minor-Second Relationship". Passages from songs of Opus 3i 6, 12, and 14 are analyzed. Chapter III i s a detailed analysis of Opus 1$, Number 5$ which applies the harmonic voice concept and attempts to expose the harmonic devices dealt with i n Chapter I I . Chapter IV i s a detailed analysis of Opus 15, Number 11. Signature of Thesis Supervisor i v CONTENTS ABSTRACT i i LIST OF ILLUSTRATIONS -v EXPLANATION OF GRAPHIC SYMBOLS USED IN THE ANALYTICAL SKETCHES x ACKNOWLEDGEMENT x i CHAPTER I. THE CONCEPT OF HARMONIC VOICE 1 CHAPTER I I . HARMONIC PROCEDURES WHICH MINIMIZE DIATONIC-CHROMATIC DIFFERENCES 18 The Tritone-Substitute (18)—The Minor-Seventh/ Augmented-Sixth Potential of "Whole-tone" chords (24)—Double-Neighbor Pairs i n "Whole-tone" and Other Contexts (30)—The Minor-Third Relationship (45)—The Minor-Second Relationship (59) CHAPTER I I I . AN ANALYSIS OF OPUS 15, NUMBER 5 . . . 70 CHAPTER IV. AN ANALYSIS OF OPUS 15, NUMBER 11 . . . 109 CONCLUSION 157 FOOTNOTES 160 SELECTED BIBLIOGRAPHY 161 V LIST OF ILLUSTRATIONS 1.0. Opus 6, Number 4, "Verlassen", measures 158. . . 5 1.1. , u n t i t l e d 6 1.2. , u n t i t l e d 6 1.3* i u n t i t l e d 6 1.4. , Progression suggested i n measures 3-4. 7 1.5* , Reduction of Example 1.4. . . 7 1 .6. , measures 9-12 8 1.7- measures 32-33 9 1.8. , measures 43-45 9 1 .9. , u n t i t l e d 10 1.10. , Vocal l i n e , measures 5-6. . . 10 1.11. , u n t i t l e d 11 1.12. , measures 4-6 11 1 .13. t u n t i t l e d 12 1.14. , u n t i t l e d 12 1.15. , u n t i t l e d 13 1.16. , measures 16-18* 13 1 .17. , measures 20-22 14 1.18. , measures 35-43 14 2.0. The harmonic-linear paradox 18 2.1. Opus 6, Number 3t measures 4-6 19 2.2. , u n t i t l e d 20 2 . 3 . , measures 21-23 22 2.4. , measures 13-16 23 2.5' , Harmonic voice summary of Example 2.4 24 2.6. (quotes from Harmonielehre) 25 2 . 7 . Opus 6, Number 3, measures 24-26 27 2.8. Opus 12, Number 2, measures 43-44 28 2 .9 . , measures 5 0 - 5 2 29 2.10. , u n t i t l e d 30 2.11. , u n t i t l e d 30 2.12. Opus 14, Number 1, measures 6-8 31 2 .13. Opus 6, Number 7» measures 5 8 - 6 5 32 2.14. , u n t i t l e d 32 2 .15. , Harmonic overstatement, measures 5 8 - 6 5 . ' 33 2.16. , u n t i t l e d ,. . 33 2 .17. , u n t i t l e d 33 2.18. Opus 14, Number 1, measures 1-3 35 2 .19. , F i r s t progression suggested, measures 1-3 35 2.20. , u n t i t l e d 36 v i 2.21. Opus 14, Number 1, second progression suggested, measures 1-3 37 2.22. , u n t i t l e d 37 2.23. , E s s e n t i a l content of measures 1-3 38 2.24. (quote from Harmonielehre) 38 2.25. (quote from Harmonielehre) . . 40 2.26. u n t i t l e d 41 2.27. Opus 14, Number 1, measures 5-8 41 2.28. , T r a d i t i o n a l progression resembling Example 2.27 42 2 . 2 9 . , "Fourth" and "Whole-tone" versions of TS(V7/V) 43 2.30. , measures 19-22 43 2.31. , u n t i t l e d 44 2.32. , u n t i t l e d 44 2.33' » Long-range manifestation of double-neighbor p a i r , D - C 45 2.34. Motion between adjacent dominant-seventh chords along the "minor-third ladder" 46 2.35. Motion between t r i t o n e - r e l a t e d dominant-seventh chords 46 2.36. Opus 6, Number 2, measures 1-14 48 2.37« » clashing voice-leadings i n measure 7« 50 2.38. , The turn to B - f l a t minor at the . beginning of measure 10 51 2.39. , Pre-dominant and dominant functions i n C - f l a t , i n measure 10 52 2.40. , B r i e f appearance of C - f l a t i n measure 11 52 2.41. Opus 12, -Number-,1, u n t i t l e d 53 2.42. ' , measures 32-42 54 2.43. , u n t i t l e d 55 2.44. , u n t i t l e d 55 2.45. , measures 36-38 56 2.46. , measures 39-42 57 2.47. , Long-range v i i o 7 functions i n D and D-flat 58 2.48. Double-neighbor and minor-seventh functions of ehharmonically equivalent chords 59 2.49. Double interpretation of an augmented t r i a d . . . 60 2.50. Opus 12, Number 1, measures 4-12 61 2.51. , u n t i t l e d 62 2.52. , Harmonic voice sketch of measures 4 to 12 of "Jane Grey". 63 2.53' t Hypothetical antecedent phrase, analogous to measures 5 to 8 of "Jane Grey", but which remains i n D minor 64 2.54. , More complex phrase, including elements which suggest F major, as i n "Jane Grey" i n measure 6 64 2.55' t Hypothetical resolution to D - f l a t major 65 2.56. , Hypothetical resolution to D minor. . 65 v i i 2.57' Opus 12, Number 1, harmonic progression analogous to that i n measures 9 and 10, but with D as the • tonic instead of D-flat 66 2.58. . , The hypothetical consequent phrase, which remains i n D minor 67 2.59' . Hypothetical close, measures 11 and 12. 67 2.60. , A possible s h i f t back to D minor i n measures 10 and 11. 68 2.61. , Return to D minor at the l a s t moment, i n measure 12. 69 3.0. Harmonic relationships i n Opus 15, Number S> • • 70 3.1. Opus 15, Number 5 71 3.2. Tonics i n Opus 15, Number 5. 73 3.3. Measures 1-2, f i r s t stage of recomposition. . . 74 3.4. Second stage of recomposition. 74 3»5« Measures 1-2, f i n a l stage of recomposition, r e s u l t i n g i n progression along the cycle of f i f t h s 75 3.6. Measures 3-4 75 3>7« "4-3" motion i n measure 3 and a s i m i l a r inference i n measure 5 77 3.8. Measures 5-6, approach to V7 of D. 77 3.9. Measures 5-6 i n harmonic voice notation. . . . 78 3.10. Prototypical approach to V7 of D 78 3.11. u n t i t l e d 79 3.12. u n t i t l e d 79 3.13. u n t i t l e d 79 3.14. u n t i t l e d 80 3.15' Rhythmic patterns of the vocal l i n e i n measures 1-2, 3-4, 5-6, and 7-9 82 3.16. Comparison of the melodic contour of the vocal phrase i n measures 5-6 with that i n 7-9 82 3.17. Hypothetical two-measure vocal phrase. . . . . 83 3.18. Two-measure groups i n the piano accompaniment, measures 7-8 and 9-10. 83 3.19. Harmonic voice summary of measures 7-10. . . . 84 3.20. Prototypical progressions having the same outer voices as i n the ultimate reduction of measures 9 and 10. 85 3.21. u n t i t l e d 85 3.22. The h i n t of TS(V7/v) i n D, brought on by the pitches B - f l a t , D, and G-sharp i n measure 10. . 86 3.23. The equivalence between l|>7 of B - f l a t and TS(V7/V) of D 87 3.24. The hint of V7 of B i n measure 10 87 3.25. Continuation of Example 3.14 from page 80. . . . 88 3.26. The prolongation of a B - f l a t major-minor-seventh chord i n measures 10 to 12 89 3.27. The vocal phrases of measures 1-2 and 13-15. . . 90 3.28. u n t i t l e d 92 3.29. u n t i t l e d „ 92 3.30. Harmonic voice summary of measures I3-I5, to be. compared with Example 3.29 93 v i i i Double appoggiatura figures from measures 6 and 8 , and measure 14. 9 4 3 . 3 2 . Measures 1 - 3 and 1 3 - 1 5 compared. 9 5 3 . 3 3 . Continuation of Example 3 . 2 5 , page 80 9 6 3 . 3 4 . u n t i t l e d 9 6 3 « 3 5 ' Measures 1 5 to 18; the suggestion of a cadence to the B tonic. 97 3 . 3 6 . Measure 14, beats 2 and 3» and measures 15 to 16; the suggestion of V-I progressions i n B. . . . 9 9 3 0 7 ' The "deceptive" cadence e f f e c t i n measures 14-15 and 17-18 9 9 3 . 3 8 . u n t i t l e d 100 3 . 3 9 . The vocal l i n e i n measures 16 to 18. 1 0 0 3.40. Measures 15-18, with emphasis upon the B - f l a t -r e l a t e d harmonic voices. 101 3.41. Functional harmony i n r e l a t i o n to G i n measures 15-18 104 3 . 4 2 . The amalgamation of Examples 3 - 3 5 , 3.40, and 3.41 1 0 5 3 . 4 3 . The "whole-tone" chord of measures 16-18, and the presence therein of the roots, third s , and sev-enths of major-minor-seventh chords on B, F, and G. 1 0 6 3 . 4 4 . Harmonic voice summary of Opus 1 5 i Number 5* • • 1 0 ? 3 . 4 5 . u n t i t l e d 1 0 8 4 . 0 . Harmonic voice motions from B - f l a t to B-natural and D - f l a t to D-natural i n measure 1 . . . . . . 110 4 . 1 . Opus 1 5 , Number 11 I l l 4 . 2 . u n t i t l e d 114 4 . 3 . u n t i t l e d 114 4 . 4 . u n t i t l e d 1 1 5 4 . 5 . u n t i t l e d 1 1 5 4 . 6 . The functions TS(V7/V) and V7 i n F-sharp. . . . 117 4 . 7 . u n t i t l e d 118 4 . 8 . u n t i t l e d 119 4 . 9 . u n t i t l e d 120 4 . 1 0 . u n t i t l e d 121 4 . 1 1 . u n t i t l e d 121 4 . 1 2 . The hint of v/lY and IV i n F-sharp, i n measures 7 and 8 1 2 2 4 . 1 3 . u n t i t l e d ,. 1 2 3 4.14. Minor t r i a d s moving to diminished t r i a d s i n measures 1 and 8 , r e s u l t i n g i n the functions v i i o 7 and v i i o 7 / V i n F-sharp, respectively. . . 124 4 . 1 5 « Harmonic voice summary, measures 8 - 1 2 . . . . . 1 2 5 4.16. u n t i t l e d 127 4 . 1 7 . u n t i t l e d 127 4.18. Piano, l e f t hand of measures 2 to 5 . . . . . . 127 4 . 1 9 . Close-up of structures (b) and (c) 1 2 8 4 . 2 0 . u n t i t l e d 128 4 . 2 1 . u n t i t l e d 129 4 . 2 2 . u n t i t l e d 131 i x 4.23« Melodic p a r a l l e l between measures 1-5 and 13-16 133 4.24. Harmonic voice summary, measures 13-14 134 4.25. Double-neighbor "fourth" chords i n the piano treble of measure 14 135 4.26. u n t i t l e d 137 4.27. u n t i t l e d 138 4.28. u n t i t l e d 138 4.29. Progression along the cycle of f i f t h s i n measures 15 and 16 140 4.30. u n t i t l e d 142 4.31. u n t i t l e d 142 4.32. u n t i t l e d 143 4.33. u n t i t l e d 143 4.34. u n t i t l e d 145 4.35» Harmonic voice summary of the vocal and piano parts i n measures 16 to 19 • 146 4.36. The expectation of a "4-3" resolution i n measures 16-17 148 4.37. u n t i t l e d 149 4.38. u n t i t l e d 149 4.39. Approach to dominant-seventh of F-sharp, comparable to events i n measures 16 to 19. • • 150 4.40. u n t i t l e d 150 4.41. Hypothetical and actual runs compared. . . . . 151 4.42. u n t i t l e d 152 4.43. u n t i t l e d 153 4.44. (1) The embellishment of I by ii7 and #ii?f as i n measures 8 and 9; (2) The t r a d i t i o n a l cadence along the cycle of f i f t h s . 154 4.45. Harmonic voice summary of measures 21-24. . . . 155 5.0. Two "equivalent" progressions along the cycle of f i f t h s i n C 158 X EXPLANATION OF GRAPHIC SYMBOLS USED IN THE ANALYTICAL SKETCHES 1. X i n place of a note-head. This means that the p i t c h i s implied. The j u s t i f i c a t i o n f o r the i m p l i c i t presence of a given p i t c h w i l l be made during the discussion of the sketch i n which that pitch appears. 2. Diagonal l i n e s drawn through regular or "X" note-heads ( >#" and ,^*f ). These serve to mark the end of a harmonic voice which i s car r i e d on i n another octave or not at a l l . 3 . Stems. These are occasionally used to aid i n the d i f f e r e n t i a t i o n of harmonic voices. The same di r e c t i o n of stem indicates membership i n the same harmonic voice. However, sometimes where several voices are i n operation, more than one may be given upward or downward stems, so that one must look f o r the proper semi-, whole-, and common-tone connections which characterize allcharmonic voices, i n addition to observing the directions of stems. k. Ties. These join pitches which continue to sound either because they are r e i t e r a t e d or because they are ac t u a l l y sustained. 5 . Brackets or parentheses ( H or ( ) ). These are used at the end of a sketch to enclose a chord which i s not actually stated i n the passage with which the sketch deals, but which helps the reader to grasp the harmonic context i n which the sketch i s conceived. The chord i n brackets or parentheses might arrive within the next few measures, or never occur. 6. "TS". This stands f o r "tritone-substitute". The term i s explained on pages 18-20. x i ACKNOWLEDGEMENT I wish to express my gratitude to Wallace Berry, my thesis supervisor, whose thorough scrutiny of my tentative analyses l e d to t h e i r c l a r i f i c a t i o n , and whose suggestions concerning general matters of sty l e and organization were invaluable. I also extend my sincerest thanks to William Benjamin, whose intere s t i n my work gave me the confidence to complete t h i s study. The excerpts of Schoenberg's works which appear i n th i s thesis are used by permission of Belmont Music Publishers, Los Angeles, C a l i f o r n i a 90049-1 CHAPTER I THE CONCEPT OF "HARMONIC VOICE" The a n a l y t i c a l s k e t c h e s i n t h i s s t u d y r e l y upon a pr o c e d u r e o f s i m p l i f i c a t i o n d e s i g n e d t o b r i n g r e g i s t r a l l y , r h y t h m i c a l l y , and h a r m o n i c a l l y complex music i n t o a form which i s more e a s i l y a c c e s s i b l e t o the t o n a l l y t r a i n e d e a r . I n v o l v e d i n t h i s p r o c e d u r e a r e t h r e e ways o f m a n i p u l a t i n g t h e m u s i c : the f i r s t e l i m i n a t e s o c t a v e d o u b l i n g s and d i s -p l a c e m e n t s so t h a t each p i t c h - c l a s s i s r e p r e s e n t e d by one p i t c h ; t h e second r e g u l a t e s the r h y t h m i c a c t i v i t y by v e r t i -c a l l y s t a c k i n g a r p e g g i a t e d chords and e l i m i n a t i n g r e p e a t e d p i t c h e s so t h a t a c h o r a l e - l i k e t e x t u r e r e s u l t s ; t h e t h i r d , and most i m p o r t a n t , i n t r o d u c e s r e g i s t r a l changes which make app a r e n t t h e common-, sem i - , and whole-tone c o n n e c t i o n s be-tween a d j a c e n t v e r t i c a l s t r u c t u r e s i n a way which i s l o g i c a l i n terms o f t o n a l c o u n t e r p o i n t . These t h r e e m a n i p u l a t i o n s r o b t h e music o f e v e r y t h i n g b u t i t s h a r m o n i c - c o n t r a p u n t a l i n t e r e s t , and y e t , the p i e c e s o f Opus 15 w i t h s t a n d such t r e a t m e n t w e l l t many o f the a n a l y t i c a l s k e t c h e s may be p e r -formed w i t h m u s i c a l c o n v i c t i o n , p r o v i d i n g p o w e r f u l t e s t i m o n y t o t h e i n t e n s i t y w i t h which u n d e r l y i n g t o n a l p r o g r e s s i o n s a f -f e c t t h e emotions o f t h e l i s t e n e r / p e r f o r m e r . The t h i r d o f the a f o r e m e n t i o n e d m a n i p u l a t i o n s r e s u l t s 2 i n t h e c o n c e p t o f "harmonic v o i c e " . The term i s i n t e n d e d to b l u r the d i s t i n c t i o n o f t e n made between harmony and c o u n t e r -p o i n t as t h e " v e r t i c a l " and " h o r i z o n t a l " a s p e c t s o f m u s i c . A c c o r d i n g t o t h i s d i s t i n c t i o n , we e v a l u a t e the harmonic f u n c -t i o n o f a c h o r d by d e t e r m i n i n g i.ts r o o t ; i f t h i s cannot be done, we t r y t o j u s t i f y t h e c h o r d as p a r t o f a c o n t r a p u n t a l m o t i o n w h i c h , depending upon t h e composer and t h e work, we may o r may n o t e x p e c t t o r e f l e c t t h e consonance/dissonance c o n c e p t s o f c o n v e n t i o n a l t o n a l i t y . A n a l y s e s which a r e r o o t -ed i n t h i s way o f t h i n k i n g t e n d t o c o n s i s t o f p r o g r e s s i o n s o f d i s c r e t e c h o r ds r e p r e s e n t e d by Roman numerals; l i n k i n g the c h o r d s a r e u n c e r t a i n s t r u c t u r e s c o n s i d e r e d t o be o f l i n e a r o r i g i n . As we become accustomed t o c e r t a i n s p e c i f i c t y p e s o f l i n e a r a l l y - c o n c e i v e d s t r u c t u r e s , we f e e l the need t o g i v e them s t a t u s as l e g i t i m a t e harmonies. The f a c t t h a t we would c o n s i d e r a q u e s t i o n such as whether t h e " c o r r e c t " r o o t o f an a u g m e n t e d - s i x t h c h o r d which p r e p a r e s a dominant i s t h e s u p e r -t o n i c , t h e sub-dominant, o r even t h e sub-mediant, e x e m p l i f i e s o u r d e s i r e t o t r a n s f e r a s t r u c t u r e from the l i n e a r w o r l d t o th e harmonic once i t has become f a m i l i a r t o us i n a c e r t a i n t o n a l c o n t e x t . Ways o f d e s c r i b i n g music which r e l y upon harmonic-c o n t r a p u n t a l d i s t i n c t i o n s a r e , p e r h a p s , adequate i n c a s e s where most v e r t i c a l s t r u c t u r e s f a l l w i t h o u t q u e s t i o n i n t o t h e "harmonic" c a t e g o r y ; however, i n Schoenberg's music be-tween Opus 1 and Opus 15, r o o t p r o g r e s s i o n s , p a r t i c u l a r l y a t t h e f o r e g r o u n d , a r e n o t u s u a l l y made o b v i o u s by a bass l i n e 3 o r by the p r e s e n c e o f p u r e l y c o n v e n t i o n a l c h o r d s . T h e r e f o r e , i f we w i s h t o determine t h e r o o t s o f c h o r d s , t h e y must some-t i m e s be i n f e r r e d from complexes o f semi- and w h o l e - t o n a l v o i c e - l e a d i n g w i t h which t h e y a r e a s s o c i a t e d . A s i m p l e ex-ample would be t h a t t h e l a t t e r appears i n a s u i t a b l e c o n t e x t , namely a passage which a t l e a s t h i n t s a t a C t o n a l i t y . I n t h i s c a s e , t h e i n -f e r r e d r o o t p r o g r e s s i o n c o n t r i b u t e s t h e p i t c h G towards a t h i r d harmonic v o i c e , the r e s u l t i n g t h r e e b e i n g I t i s i m p o r t a n t t o n o t e t h a t t h e p r o g r e s s i o n o f r o o t s , which i s G t o C i n t h i s c a s e , does n o t comprise a s i n g l e harmonic v o i c e ? r a t h e r , each r o o t i s p a r t o f w h i c h e v e r harmonic v o i c e l e a d s t o and/or f o l l o w s from i t by common-, semi-, o r whole-tone s u c c e s s i o n . I n f e r r i n g a r o o t p r o g r e s s i o n r e s u l t s i n th e i m p l i c a t i o n o f f u r t h e r harmonic v o i c e s which may be com-p l e t e d t o form the t h r e e - o r f o u r - p a r t t e x t u r e r e q u i r e d t o d i s p l a y t r i a d s and s e v e n t h chords i n f u l l . T h i s p r o c e s s o f i n f e r r i n g and c o m p l e t i n g a p r o g r e s s i o n i s u s e f u l when one i s d e a l i n g w i t h Schoenberg's s p a r s e r t e x t u r e s , and might be de-s c r i b e d a p t l y as "harmonic o v e r s t a t e m e n t " . I t i s a l s o use-f u l i n t h e c o n t e x t o f a t h i c k t e x t u r e i n which o n l y c e r t a i n m M. i s i n f e r r e d from 4 A o when 4 o f the v o i c e s f o l l o w t y p i c a l t o n a l p a t t e r n s , o r i n which p a t t e r n s a s s o c i a t e d w i t h more t h a n one f a m i l i a r p r o g r e s s i o n seem t o be combined; i n such c a s e s , the v o i c e s i m p l y i n g the p r o g r e s s i o n ( s ) which one d e s i r e s t o emphasize may be e x t r a c t -ed from t h e t o t a l t e x t u r e and a d d i t i o n a l v o i c e s i n f e r r e d t o complete i t ( t h e m ) where n e c e s s a r y . The f o l l o w i n g sample a n a l y s i s s e r v e s t o i n t r o d u c e the c o n c e p t o f harmonic v o i c e as i t w i l l be a p p l i e d t o p i e c e s from Opus 15• p a r t i c u l a r l y w i t h r e g a r d t o t h e drawing out o f t o n a l p r o g r e s s i o n s from v o i c e - l e a d i n g complexes which im-p l y them. How do we h e a r t h e o p e n i n g measures o f Opus 6, Number 4, " V e r l a s s e n " ? A l t h o u g h some would i n t e r p r e t measures 1 t o 6 as e x p r e s s i n g o n l y one harmonic f u n c t i o n ( i i n E - f l a t m i n o r ) , s u b t l e f o r e g r o u n d p r o g r e s s i o n s are i n f e r r a b l e from t h e m o t i o n o f t h e harmonic v o i c e s o v e r t h e E - f l a t p e d a l - p o i n t . F u r t h e r -more, t h e s e p r o g r e s s i o n s a r e f i t t i n g f o r t h e o p e n i n g measures o f a p i e c e , c o n s i s t i n g o f m o t i o n t h r o u g h t o n i c , dominant-pre-p a r a t o r y , and dominant f u n c t i o n s — a f t e r the f a s h i o n o f the t y p i c a l i n t r o d u c t o r y p r o g r e s s i o n s , I-IV-V? and I-ii7- v7. The two harmonic v o i c e s which a r e r e p e a t e d f o r t h e f i r s t f i v e measures o f t h e p i e c e a r e shown i n Example 1.1; Example 1.2 shows th e s l i g h t l y a l t e r e d v e r s i o n o f t h o s e v o i c e s which oc-c u r s i n measure 6; Example 1.3 shows the t o n a l p r o g r e s s i o n which we a r e reminded o f when we h e a r t h e p r e c e d i n g two Ex-amples . 5 Example 1.0: Opus 6,-Number 4, " V e r l a s s e n " , measures 1-8. 6 Example 1.1: measures 1 to 5 Example 1.2* M I f f b f ^ J f measure 6 (Example 1.3: 7' > v ? * I f f r ^ s Z b y E ^ - i V7/VI \1 1 V 1 o r i i 7 v ? tjX I f N A harmonic progression very s i m i l a r to that shown i n Example 1.3 i s suggested when the vocal phrase of measures 3 and 4 i s stated above the two harmonic voices of Example 1.1. This progression, which i s shown i n Example 1.4, d i f f e r s from that i n Example 1.3 only i n the substitutions of B-double-flat fo r B - f l a t and D-double-flat for D- f l a t , which are made to create a si m i l a r emphasis i n the accompaniment upon A-natural and C-natural to that which exists inaithe vocal phrase. It should be noted that the whole-notes i n Example 1.4 represent the pitch-classes found i n the vocal phrase of measures 3 and 4. The e f f e c t created when one sings the vocal phrase while performing Example 1.4 i s t r u l y one of harmonic over-statement, as can be v e r i f i e d by analysis of that example and re-ference to other passages i n "Verlassen". In Example 1.5» a reductive procedure has been applied to Example 1.4 which suggests that one harmony, c e r t a i n l y not i i n E - f l a t minor, i s being prolonged. Example 1.4: Progression suggested i n measures 3-4. / / $0 1 ty* 4°= Example 1 . 5 : Reduction of Example 1 .4 5 ^ /Example 1 .5 contains a l l of the pitch-classes of the vocal phrase i n measures 3 and 4, with the exception of E - f l a t ; i n addition, i t contains the important motion from E to D with which the vocal phrase begins, making i t , i n e f f e c t , a chordal 8 version of the vocal phrase. This creates a strong case for the appropriateness of the in f e r r e d B-double-flat and D-double-f l a t at the beginning of measure 3 and suggests that l i k e i n -ferences might be made, i n retrospect, at the beginnings of measures 1 and 2. The r e s u l t i n g interpretation of measures 1 to 3 as representing D major-minor-seventh chords embel-l i s h e d with upper-neighbor-tone motions from E to D i s strongly supported by the appearance, i n measures 9 and 11 respectively, of s i m i l a r l y treated A and G-fl a t major-minor-seventh chords (Example 1.6). Furthermore, l a t e r pas-Example 1.6: Opus 6, Number 4, measures 9-12' h-4f ». Er y r a - len wa J.. j) J r mir das Herz vei p - . dor t _ h , J JH=| fcK 11> L I IT-fc f|3 r • «p h j J vm % i $4 — 1 I f * — $ • JjJ I n I j j j j j j — 1 i iJN ' .b,i, - • h 1 N = tea \— die L i p / J'. h i , , 1 j -pe spra ch ke in 1 "' ¥ Ab - schieds - wo r t _ si 4— e 8' 1 4 # = r i i l f t > 12 F- _/ —r-p—| j ~ — | "t ^ " ~ ~ — [il Example 1.6, continued measures 1 to 3 measure 9 measure 11 sages i n the song reveal f u l l y r e a l i z e d implications of the D major-minor-seventh harmony which were inherent i n the i n i -t i a l harmonic voices of Example 1.1 (Examples 1.7 and 1.8). Example 1.7: Opus 6, Number 4, measures 32+33« Example 1.8« Opus 6, Number 4, measures 43-45. Langsam. nr di Was war mir der pran-gen-de \pp 11 i J W J j ) hi. - -10 The D major-minor-seventh chord with minor-ninth which occurs i n measures 33 and 43-44 r e l a t e s to the ^ version of D major-minor- seventh which occurs over the E - f l a t pedal-point i n the i n i t i a l measures of the piece by a simple exchange of out er voices (Example 1.9)• The juxtaposition of these two ex-pressions of D-major-minor-seventh harmony which occurs i n measure 44 and 45 of Example 1.8 makes th e i r r e l a t i o n s h i p c l e a r . ^Example 1.9* * y * - f4- f-^ measures 1-6 3,2-03 45-48 43-44 Wher.eas the f i r s t vocal phrase, i n measure 3 and 4, enabled us to i n f e r the progression i n Example 1.4, the second vocal phrase connotes a s l i g h t l y d i f f e r e n t foreground progression due to the presence of C - f l a t at the beginning of measure 5« The second vocal phrase i s shown i n Example 1.10. Example 1.10: Vocal l i n e , measures 5 -6 . r , j n . f—6—^ «* iw 4 ) 11 During measures 1 to 5 , a d e f i n i t e sense of E - f l a t as the tonic i s created through the p r e v a i l i n g E - f l a t pedal-point and the foreground harmonic progression i n E - f l a t minor in f e r r e d i n Example 1.3 (page 6 ) ; r e s u l t i n g from t h i s i s the l i s t e n e r ' s desire to hear the chromatically r i s i n g harmonic voice (Example reach B - f l a t , forming a perfect f i f t h with the E - f l a t pedal-point, on the f i r s t beat of each new measure. Therefore, the C - f l a t which i n i t i a t e s the vocal phrase i n measure 5 i s heard as an upper neighbor to B - f l a t and, when aural l y connected with A-natural from measure 4 and the minor t h i r d , E - f l a t - G-f l a t , with which i t occurs on the f i r s t beat of measure 5» r e s u l t s i n the hint of an augmented-sixth function embellishing the b r i e f E - f l a t major harmony which follows (Example 1 . 1 2 ) . Example 1.12: Opus 6, Number 4, measures 4-6. Shown are those pitches from which the "harmonic overstatement"' i n the following portion of t h i s example i s inf e r r e d . the 1.11) Pfo t 1* b. b, 1 2 Example 1 . 1 2 , c o n t i n u e d . Harmonic o v e r s t a t e m e n t o f Opus 6, Number 4, measure 4-6. r E - f l a t : A u g6 — j i v o r i i 7 — V 7 / V I - - l ) 7 — i v — V 7 o r i i 7 I n a d d i t i o n t o the l o c a l a ugmented-sixth f u n c t i o n which o c c u r s a t t h e b e g i n n i n g o f measure 5» t h e e n t i r e meas-ur e can be h e a r d as e x p r e s s i n g the c h o r d i n Example 1.13* Example 1 . 1 3 s As shown i n Example 1.14, the o u t e r v o i c e s o f measure 5 range from C - f l a t t o G - f l a t and G - f l a t t o A - n a t u r a l , b o t h b e i n g accom-p a n i e d by t h e c o n s t a n t E - f l a t p e d a l - p o i n t . The r e s u l t a n t c h o r d , Example 1.14: **1 to with i t s enharmonic equivalent (Example 1.1$), Example 1 . 1 5 s K . ^ i s important throughout the piece i n a var i e t y of ways: ( 1 ) i t establishes a voice-leading connection between the important D major-minor-seventh chord and the major version of the tonic t r i a d , E - f l a t (Example 1.16, and Example 1 . 1 2 from the end of measure k to beat 2 of measure $); ( 2 ) i t embellishes the domi-Example 1.16: Opus 6, Number 4, measures 16-18. ; nant-seventh of E - f l a t (Example 1 . 1 7 ) ; ( 3 ) i t i s given a hint of emphasis as a tonic i n the middle of the piece (Example 1.18). 14 Example 1.17« measures 2 0 - 2 2 ' E - f l a t s V#5 A u g 6 E - f l a t s V #5' -Aug 6 '#5 Example 1.18» measures 3 5 - 4 3 . l l t U l . > H - u- ..1 |l>, Iff) y P 1 ? * a 4 is sam Pas - sen! 35 j f r ( c o n t i n u e d on page 15) Example 1.18, c o n t i n u e d . Man - lich wur - de die Welt nun .•v nnr^r itf 33 . ^ F - T ^ . — . 37 C - f l a t s V' I ( V I ) I ^ 7 V^ _ p a s s i n g t o V 7 i i #7 v? - p a s s i n g t o V 16 The voice-leading which connects the C - f l a t chord of measure 41 with the D major-minor-seventh chord of measure 43, C - f l a t to C-natural and E - f l a t to D , exemplifies a par-t i c u l a r a f f i n i t y of Schoenberg for connecting chords whose roots l i e a minor-third apart; i t should he noted that Ex-ample 1.4 of page 7 depicts one complete progression i n -ferred from harmonic voices i n the opening measures of „ "Verlassen", revealing a harmonic sequence consisting of chords connected i n t h i s manner ( G I * 7 to E^ 7 and F 7 to D 7 ) . Henceforth, the term "minor-third r e l a t i o n s h i p " w i l l he ap-p l i e d to t h i s type of connection; i t w i l l be treated as a separate topic l a t e r , as i t s r o l e i n Opus 15 i s very impor tant. Example 1.18 displays harmonic voice notation as i t generally w i l l be applied to Opus 15* One problem a r i s i n g from t h i s type of notation must be mentioned: pitches which may move i n either of two directions, such as the f i f t h s of chords moving along the cycle of f i f t h s , involve an ambigui-ty which cannot be resolved here. Of the greatest concern i n t h i s study are those pitches which are strongly directed, such as the major thirds and minor sevenths of chords moving along the cycle of f i f t h s . In cases where the tendency of a p i t c h i s l e s s s p e c i f i c , the a n a l y t i c a l sketches w i l l show both possible motions, assuming that, i n an abstract sense, both may be said to occur. The concept of harmonic voice, as i l l u s t r a t e d i n the preceding examples, leads to a certain kind of equality be-17 tween d i a t o n i c and c h r o m a t i c p r o g r e s s i o n s , s i n c e t h e common-, semi-, and whole-tone c o n n e c t i o n s which both p o s s e s s , as op-posed t o t h e r o o t s which s u p p o s e d l y l e n d g r e a t e r harmonic v a -l i d i t y t o d i a t o n i c p r o g r e s s i o n s , a r e emphasized. T h i s " e q u a l -i t y " i s e x p l o i t e d by Schoenberg t h r o u g h s e v e r a l g e n e r a l h a r -monic p r o c e d u r e s , a l l o f which a re f o u n d i n p r o f u s i o n i n t h e Opus 15 songs. These p r o c e d u r e s w i l l now be i n t r o d u c e d i n c o n t e x t o f e a r l i e r , more o v e r t l y t o n a l songs, where t h e y may be a s s i m i l a t e d r e a d i l y i n p r e p a r a t i o n f o r a p p r o a c h i n g t h e i r l e s s e x p l i c i t o c c u r r e n c e s i n Opus 1$. 18 CHAPTER II HARMONIC PROCEDURES WHICH MINIMIZE DIATONIC-CHROMATIC DIFFERENCES The Tritone-Substitute The most basic p o t e n t i a l which the tri t o n e possesses i s to imply a l o c a l dominant-seventh function having one of two possible roots, themselves l y i n g a tr i t o n e apart. Hence, the paradox exists that descending perfect f i f t h s and descend-ing semitones are simultaneously implied as the roots of chromatically descending tri t o n e s , the former being associat-ed with everything that i s "harmonic" and the l a t t e r with everything that i s " l i n e a r " . Example 2.0s The harmonic-linear paradox Two cycles of f i f t h s , a t r i t o n e aparts Possible rootst Possible roots: Two chains of semitones, a t r i t o n e apart: -A tP**—b» ^ — a t , — i ' — 7 — ^ Possible roots: i ~- — />' - * N # mw Possible roots: 1 — t -h-P # - « =#= — 19 T h i s c o n f l i c t between t h e harmonic and the l i n e a r i s r e s o l v e d i n Schoenberg's m u s i c , s i n c e he f r e e l y i n t e r c h a n g e s t h e two r o o t s a t t r i b u t a b l e t o a g i v e n t r i t o n e , l e a v i n g i t t o t h a t t r i t o n e t o d e f i n e t h e l o c a t i o n a l o n g t h e c y c l e o f f i f t h s i n w h i c h e v e r key i s b e i n g i m p l i e d a t t h e moment. An e x c e l l e n t example o f t h e i n t e r c h a n g e a b i l i t y o f r o o t s w hich l i e a t r i t o n e a p a r t i s f o u n d i n Opus 6, Number 3» "Mad-c h e n l i e d " . Example 2.1s Opus 6, Number 3» measures 4-6. I n t h i s example, r o o t s o f chords a r e shown as stemmed p i t c h e s , below t h e f o u r harmonic v o i c e s . I n measures 5 and 6, D and A - f l a t , t h e two p o s s i b l e r o o t s o f the t r i t o n e , F - s h a r p / G - f l a t - C, a r e s t a t e d , p r o l o n g i n g a dominant f u n c t i o n i n G. The A - f l a t m a j o r - m i n o r - s e v e n t h c h o r d which o c c u r s h a l f w a y 20 t h r o u g h measure 5 can be c a l l e d t h e " t r i t o n e - s u b s t i t u t e " o f 7 V o f G, s i n c e i t c o n t a i n s t h e t r i t o n e formed by t h e t h i r d and s e v e n t h o f V , w i t h t h e a l t e r n a t e r o o t t h e r e o f , A - f l a t . The t r i t o n e - s u b s t i t u t e o f a g i v e n c h o r d h e n c e f o r t h w i l l be i n d i c a t e d by a "TS", f o l l o w e d by t h e Roman numeral r e p r e s e n t -i n g t h e harmonic f u n c t i o n o f t h a t c h o r d , as i n measure 5 o f Example 2.1. V a c i l l a t i o n between a c h o r d and i t s t r i t o n e - s u b s t i t u t e r e p r e s e n t s no change i n harmonic f u n c t i o n when we t h i n k i n terms o f harmonic v o i c e m o tions r a t h e r t h a n r o o t p r o g r e s s i o n s . The most s t r o n g l y d i r e c t e d harmonic v o i c e m o t i o n s which o c c u r 7 d u r i n g a p r o g r e s s i o n from V t o I a r e t h o s e from the l e a d i n g -tone t o t h e t o n i c and t h e subdominant t o t h e mediant p i t c h e s } t h e s e m o t i o n s a r e a l s o p r e s e n t i n a p r o g r e s s i o n from TS(V^) t o I . F u r t h e r m o r e , a b s o l u t e i d e n t i t y o f p i t c h - c l a s s c o n t e n t between any m a j o r - m i n o r - s e v e n t h c h o r d and i t s t r i t o n e - s u b s t i -t u t e may be a c h i e v e d s i m p l y by l o w e r i n g t h e f i f t h s o f each c h o r d , making them d i m i n i s h e d ; s i n c e , i n terms o f harmonic v o i c e m o t i o n , t h e f i f t h s and r o o t s o f m a j o r - m i n o r - s e v e n t h c h o r d s a r e n o t s t r o n g l y d i r e c t e d , as a r e t h e t h i r d s and sev-e n t h s , such a l t e r i n g o f f i f t h s has no i m p o r t a n t e f f e c t on the harmonic v o i c e m o t i o n s which i s s u e f rom such c h o r d s . I n Example 2.1, t h e symbol, " i i ' ? " , which i s used t o r e p r e s e n t t h e c h o r d (Example 2.2) Example 2.2« i n measures 3 and k i s i n t e n t i o n a l l y made more g e n e r a l t h a n i t 21 m i g h t be. The passage i n q u e s t i o n p r e s e n t s us w i t h i n f l e c -t i o n s o f b o t h the major and minor modes o f G, r a i s i n g t h e i s -sue o f whi c h mode governs t h e i n d i c a t i o n o f c h r o m a t i c a l t e r a -t i o n s t o c h o r d s b e s i d e t h e i r c o r r e s p o n d i n g Roman nu m e r a l s . I n Example 2.1, one i s tempted t o s p e c i f y t h e mode o f G as major because t h e o p e n i n g t o n a l i t y o f " M a d c h e n l i e d " i s E mi n o r and a s h i f t t o t h e r e l a t i v e major key i s such a common harmonic g e s t u r e ; however, the i i ' 7 f u n c t i o n i n measures 3 and 4 i s d i a -t o n i c t o t h e m i n o r mode o f G, a f a c t which i s i n d i c a t i v e o f Schoenberg's c a s u a l a t t i t u d e t o w a r d major/minor d i s t i n c t i o n s . We would be p l a c i n g f a r g r e a t e r emphasis upon such d i s t i n c t i o n s t h a n t h e composer i f we i n s i s t e d upon s p e c i f y i n g the key as G major and t h e f u n c t i o n as " i i u Z " . I n s t e a d , t h e " n e u t r a l " sym-7 b o l , " i i f " , s u f f i c e s , and we u n d e r s t a n d the key t o be a m i x t u r e o f G major and minor a t t h i s p o i n t i n t h e p i e c e . I n Example 2.1, t h e concept o f t h e t r i t o n e - s u b s t i t u t e was i n t r o d u c e d w i t h the s p e c i f i c f u n c t i o n , TSfV' 7). T h i s f u n c -t i o n i s n o t t o be c o n f u s e d w i t h t h a t o f the " N e a p o l i t a n " c h o r d , w h i c h does n o t c o n t a i n t h e c r u c i a l t r i t o n e needed t o r e s o l v e t o t h e r o o t and t h i r d o f t h e t o n i c t r i a d and, t h e r e f o r e , r e -t a i n s t h e q u a l i t y o f a pre-dominant harmonic s t a g e , o r a t r u e "1?II". F o r example, a " N e a p o l i t a n - t o - v ' ' " p r o g r e s s i o n o c c u r s l a t e r i n "M a d c h e n l i e d " . I n measure 21, one has t h e sense o f two s e p a r a t e harmonic f u n c t i o n s , t h e f i r s t pre-dominant and th e n e x t dominant (Example 2.3)} t h i s s i t u a t i o n i s c o m p l e t e l y d i f f e r e n t from t h a t i n Example 2.1, where a p l a y f u l t o s s i n g back and f o r t h o f D and A - f l a t beneath the c o n s t a n t F - s h a r p / G - f l a t and C p r o l o n g e d a p u r e l y dominant f u n c t i o n . 22 Example 2.3* Opus 6, Number 3, measures 21-23. Ct |? II V 7 1 V 7/IV IV The triton e - s u b s t i t u t e with which we have been long-est aquainted i s , of course, the augmented-sixth chord which prepares the dominant, of TS(V 'Vv ) . It i s distinguishable from VI of the minor mode or JPVI of the major because, unlike those t r i a d s , i t contains the same tr i t o n e as V^/V; since the most important harmonic voice motions which proceed from V^/V do so from i t s t h i r d and seventh, which form t h i s t r i t o n e , TS(V'V'V) may be said to have e s s e n t i a l l y the same harmonic function as V?/V. The d i s t i n c t i o n between TSCV^/V) and the sub-mediant chord i s made i n examples 2.4 and 2.5» which are taken from Opus 3» Number 2, "Die Aufgeregten". I n i t i a l l y , the D major-minor-seventh harmony i s measure 13 has a dominant function, 23 since G minor i s strongly suggested as the tonic key during the opening measures of the piece* however, i n r e l a t i o n to G-f l a t , which i s tonicized by the progression, i i 7 - V 7 - I , i n meas-ures 15 and 16, the same D major-minor-seventh harmony repre-sents the function TS(V 7/v) (Example 2 . 4 ) . What prevents us Example 2 .4 t Opus 6, Number 3 , measures I3-I6. und ein hoi - derSchmetterling zer-riss den a - zirr - - neaTrack Iin G: V GJ? t |>VI v i i i 7 V 7 1 from hearing a d i r e c t progression from TS(V 7/v) to V 7 i n G-fl a t i s the occurrence of the simple D major t r i a d , without i t s mi-nor seventh, halfway through measure 14; t h i s chord functions 24 as Wl o f G - f l a t and moves through v i and i i 7 t o r e a c h V 7 i n measure 15• T h i s l o c a l , d i a t o n i c approach t o V 7 o f G - f l a t weakens t h e more d i s t a n t r e l a t i o n s h i p between t h e t r i t o n e , C -F - s h a r p / G - f l a t , o f TS(V 7/V) and t h e r o o t and t h i r d , D - f l a t and F, o f V whi c h l i n k s measure 13 t o measure 16. A harmonic v o i c e summary o f t h i s passage i s p r e s e n t e d i n Example 2.5» i n o r d e r t o c l a r i f y p o i n t s made i n Example 2.4. Example 2.5* Harmonic v o i c e summary o f Example 2.4. 13 1 i 4 15 0 ? r — * G: T S ^ - V 7 , T S ^ J - V 7 T S ( V ^ ) - V — G|P« V£ -TS(|5).IZ - T S ( ^ ) T S t | ^ ) - ^ V I — v i — i i 7 V 7 — I 11 l l The Minor-Seventh/Augmented-Sixth P o t e n t i a l  o f "Whole-tone" Chords I n t h e "Harmonielehre , Schoenberg emphasizes t h e a r -r i v a l a t whole-tone sounds t h r o u g h common c o m p o s i t i o n a l de-v i c e s , such as m e l o d i c m o t i o n between tones o f augmented t r i a d s and c e r t a i n s e v e n t h c h o r d s , arid c h r o m a t i c a l t e r a t i o n o f conven-t i o n a l c h o r d s . He i l l u s t r a t e s t h i s v i e w w i t h s e v e r a l examples, th e most i m p o r t a n t o f which a r e qu o t e d i n Example 2.6.1 25 Example 2.6s (from Schoenberg) ( i ) Examples from H a r m o n i e l e h r e which d e p i c t melo-d i c m o t i o n between p i t c h e s o f an augmented t r i a d , r e s u l t i n g i n a whole-tone c o l l e c t i o n . 318 | l ^ t e l i t e j_«ULi U ^ ^ ( i i ) F u r t h e r examples, d e p i c t i n g m e l o d i c m o t i o n between p i t c h e s o f ma j o r - m i n o r - s e v e n t h chords w i t h r a i s e d o r m i s s i n g f i f t h s . 319 3CT b i = j j = a i p b : i ( i i i ) Examples showing the f u n c t i o n o f a "whole-tone" c h o r d as a dominant-seventh w i t h b oth r a i s e d and l o w e r e d f i f t h s , and i t s d e r i v a t i o n t h r o u g h t h e c h r o m a t i c a l t e r a t i o n o f a n i n t h c h o r d . 322 < 1° " E B B 323 3fc 26 Example 2.6, c o n t i n u e d ( i v ) The complete "whole-tone" c h o r d , as shown i n • Schoenberg's Ex. 321. Schoenberg d e s c r i b e s our a u r a l g a t h e r i n g o f a whole-tone c o l l e c t i o n i n t o a c h o r d t h u s i [TheH d e r i v a t i o n [of a whole-tone c o l l e c t i o n t h r o u g h m e l o d i c m o t i o n between c h o r d p i t c h e s ] r e f l e c t s t h e way i n which o ur e a r draws a n a l o g i e s ( k o m b i n i e r t ) t i t co n n e c t s l i k e t h i n g s , i t s e t s w i d e l y s e p a r a t e d e v e n t s a d j a c e n t t o one a n o t h e r and a d j a c e n t e v e n t s o v e r one a n o t h e r . Once t h e t h r e e f i g u r e s o f t h r e e tones shown i n Examples 318a, b, and c are a c t u a l l y used, t h e y soon move c l o s e r t o one a n o t h e r ( 3 l 8 d ) 2 a n d f i n a l l y sound t o g e t h e r a t t h e same time (321). I t i s c l e a r t h a t Schoenberg d i d n o t t h i n k o f a whole-tone c o l l e c t i o n as a p r e f a b r i c a t e d s c a l e o r c h o r d .which a com-poser' d e c i d e d t o use, b u t as an out g r o w t h o f c e r t a i n harmonic and m e l o d i c p r o c e d u r e s . S p e c i f i c a l l y o f c o n c e r n i n t h i s s t u d y a r e t h o s e harmonic p r o c e d u r e s which i n v o l v e m ajor-minor-sev-e n t h and augme n t e d - s i x t h chords i n "whole-tone" passages o f works o f Schoenberg. A s i m p l e example o f a d o m i n a n t - f u n c t i o n i n g passage which c o n t a i n s a whole-tone c o l l e c t i o n i s f o u n d i n Opus 6, Number 3» "Ma d c h e n l i e d " (Example 2.7). A t d i f f e r e n t p o i n t s i n Opus 12, Number 2, "Der v e r l o r e n e Haufen", t h e two who&e-tone c o l l e c -t i o n s f u n c t i o n as T S ( V 7 A ) i n C-sharp and V 7 i n E - f l a t ( a dom-i n a n t - p r e p a r i n g augmented-sixth c h o r d and a dominant-seventh c h o r d , r e s p e c t i v e l y ) (Examples 2.8 and 2.9). I t i s i m p o r t a n t 2? to understand that, when a complete whole-tone c o l l e c t i o n i s harmonically interpreted (that i s , a l l six members of the c o l -l e c t i o n are a c t u a l l y or i m p l i c i t l y present simultaneously), six separate harmonic voices are present, each of which resolves to a p a r t i c u l a r member of the following harmony. Even though whole-tone c o l l e c t i o n s are often accumulated during melodic whole-tone passages, as i n examples 2.7, 2.8, and 2.9» one must guard against i n t e r p r e t i n g a whole-tone scale as a single har-monic voice; instead, each new member of the scale ( i . e . of the c o l l e c t i o n ) must be interpreted as belonging to a d i f f e r e n t harmonic voice, i f the scale, indeed, functions as a chord. Example 2.7« Opus 6, Number 3» measures 24-26, Es V 7 1 (V r has major ninth, and raised and lowered f i f t h s ) 28 Example 2.8: Opus 12, Number 2, measures 43-44. j wird die Mau - er vom Bo - den ge - fegt sein yesante <—T f s **» I * TS(V 7/V) v * 5 — v i i 7 — I A more t r a d i t i o n a l v e r s i o n o f measures it* 7* *f* ™ 31 ~ ' C#s TS(V 7/V) 29 Example 2.9« Opus 12, Number 2, measures 50-52. E|?S V7 I ( w i t h m a j o r - n i n t h , r a i s e d and l o w e r e d f i f t h s ) p f t h e whole-tone's two p o s s i b l e i n t e r p r e t a t i o n s , as a major second (minor seventh) and a d i m i n i s h e d t h i r d (augment-ed s i x t h ) , t h e l a t t e r i s e s p e c i a l l y i m p o r t a n t i n c o n t e x t o f Opus 15. S i n c e t h e term "augmented-sixth c h o r d " i s s t i l l c h i e f l y used t o d e s c r i b e a dominant p r e p a r a t i o n i n t o n a l m usic, w h i l Schoenberg uses augmented-sixth chords i n many o t h e r c o n t e x t s , and because Schoenberg's c h o i c e s o f i n n e r v o i c e s w i t h i n the augmen t e d - s i x t h frame are o f t e n u n c o n v e n t i o n a l , the more gener-a l term " d o u b l e - n e i g h b o r c h o r d " has been 'chosen as an a l t e r n a -t i v e ; l i k e w i s e , the i n t e r v a l o f an augmented s i x t h , o r a d i m i n -i s h e d t h i r d , w i l l o f t e n be r e f e r r e d t o as a " d o u b l e - n e i g h b o r 30 p a i r " . By the time of Opus 15, the resolution of a double-neighbor p a i r to a unison or octave has become an exceeding-l y common way of approaching a s t r u c t u r a l l y important p i t c h -c l a s s . We w i l l now examine the double-neighbor r e l a t i o n s h i p , not only i n context of whole-tone c o l l e c t i o n s , but also with respect to "fourth chords" and ordinary minor-seventh and aug-mented-sixth chords. Double-Neighbor Pairs i n "Whole-tone"  and Other Contexts Excellent examples of the double-neighbor r e l a t i o n s h i p and i t s connection with the whole-tone c o l l e c t i o n s are found i n Opus 14, Number 1, "Ich darf nicht dankend". In measures 6 and 7, the motive given as Example 2.10, Example 2.10: "tand i t s transposition (Example 2.11), Example 2.11: create a harmonic progression from TStV^/V) to V 7 i n F-sharp, as shown i n Example 2.12. Although the l o c a l behavior of these two motives i s i d e n t i c a l , save that one embellishes C-sharp with i t s double-neighbor p a i r and the other does so f o r C-natural, 31 i n the la r g e r context of functional harmony i n F-sharp, corres-ponding parts of the motives are weighted d i f f e r e n t l y . The C-natural which i s embellished by the double-neighbor pair, B -C-sharp, i n the second motive, i s merely a lower neighbor to the C-sharp of the tonic ^ chord i n measure 7; therefore, the additional function of B - C-sharp as the seventh and root of V' i n F-sharp becomes the most important one. There i s no such ambiguity regarding the double-neighbor pair, C - D, contained i n the f i r s t motive, as i t functions only i n TS(V 7 /v), Example 2 . 1 2 s Opus 1 4 , Number 1 , measures 6 - 8 . F#s TS(V 7/V)—V 7 TS(V 7)- I (at "*", a decorative TS(V 7/V)) 32 The f i n a l measures of Opus 6, Number 7* "Lockung", ex-emplify a double-neighbor pair, i n the context of an ordinary TS(V 7), which resolves conspicuously, de-emphasizing i t s har-monic o r i g i n i n favor of the simple, s k e l e t a l resolution of a diminished t h i r d to a unison (Example 2.13)• Example 2.13: Opus 6, Number 7, measures 58-65 • [The complete harmonic context of the double-neighbor pa i r , D - F - f l a t , can be in f e r r e d from the preceding measures. The progression i n measures 58 and 59 from V 7 of G-f l a t to n Vy^ of E - f l a t involves three harmonic voice motions: C - f l a t to B - f l a t , F to F - f l a t , and D- f l a t to D, the l a t t e r two of which eventually converge on the tonic p i t c h , E - f l a t . A sketch of the most important harmonic voices i n measures 58 to 65 i s given i n Example 2.14. Example 2.14: 58 59 60 61 62 63-4 65 n» t>» b>__y* t* E|>, 1 ^ — ^ ^ - — ^ - — ^ T S ( v 7 ) ~ i ; o r i 33 The more detailed harmonic overstatement of measures 58 to 65 given i n Example 2.15 reveals that the dominant pitch, B - f l a t , i s also embellished by i t s double-neighbor pair, A - C - f l a t , although a complete TS(V 7/V) function i s not present. Example 2.15: Harmonic overstatement, measures 58-65 ( B - f l a t embellished by i t s double-neighbor pair at points " * " ) . % OR X 58 59 60 -61 -62" 63 64 65" Ebijrz— v Z — y x _ V#5 III v i i S ? TS(V 7) i or I III III ( o r n i # 5 ) 3 Of s p e c i a l i n t e r e s t i n Example 2.15 i s the p a r t i c u l a r context i n which the double-neighbor pair, A - C - f l a t , does occur, namely that of the harmonic structure i n Example 2.16. Example 2.16: This chord prepares TS(V7») as would a i i 7 chord prepare a true dominant-seventh (Example 2 . I 7 ) . Therefore, the double neigh-Example 2 . 1 ? : -b y ^ w i V r possible actual j 1 *l 0. "At i i V' — I E|?:TS(V 7)-I 34 b o r p a i r , A - C - f l a t , has a s u b t l e , a d d i t i o n a l f u n c t i o n as the major second ( o r minor s e v e n t h ) i n a c h o r d which d i r e c t l y p r e -cedes TS(V?) a l o n g the c y c l e o f f i f t h s i n A, the t o n i c a t r i t o n e away from E - f l a t . T h i s i s an e s p e c i a l l y f i n e example o f what mig h t be c a l l e d t h e " d o u b l e - n e i g h b o r / m i n o r s e v e n t h " dichotomy. An a s p e c t o f Schoenberg's harmonic v o c a b u l a r y which p l a y s an i m p o r t a n t r o l e i n Opus 15 and which r e v e a l s a n o t h e r f a c e t o f t h e d o u b l e - n e i g h b o r r e l a t i o n s h i p may be i n t r o d u c e d , f a c e t i o u s l y , by t h e " e q u a t i o n " , "4 + 4 = 6 o r 7". The i m p l i c a t i o n o f the e-q u a t i o n i s t h a t two p e r f e c t f o u r t h s s t a c k e d one upon the o t h e r a r e sometimes b e t t e r t h o u g h t o f as a s i m p l e d o u b l e - n e i g h b o r o r m i n o r - s e v e n t h c h o r d , r a t h e r t h a n as a " f o u r t h c h o r d " . T h i s i s because the i n t e r v a l f r a m i n g such a s t r u c t u r e e x h i b i t s s t r o n g v o i c e - l e a d i n g t e n d e n c i e s ( i n Opus 15 and e a r l i e r works) which one e a s i l y h e a r s i n t o n a l t e rms: s e m i - t o n a l convergence o f the o u t e r v o i c e s s u g g e s t s a r o o t p r o g r e s s i o n down a minor t h i r d , o f -t e n t o a n o t h e r s e v e n t h c h o r d , and s e m i - t o n a l d i v e r g e n c e s u g g e s t s an a u g m e n t e d - s i x t h o r d o u b l e - n e i g h b o r r e s o l u t i o n . Both v o i c e -l e a d i n g p a t t e r n s a r e so f a m i l i a r t o t h e t o n a l l y - t r a i n e d l i s t e n e r t h a t t h e y can o v e r r i d e t h e l e s s f a m i l i a r a c t i v i t y o f i n n e r v o i c -es i n c e r t a i n c o n t e x t s . I n measures 1 t o 3 o f Opus 14, Number 1, f a m i l i a r sounds r e s u l t from t h e p r e s e n c e o f harmonic v o i c e m o tions f o u n d i n two t r a d i t i o n a l p r o g r e s s i o n s ? The f i r s t i n v o l v e s a c o n v e r g i n g minor s e v e n t h w h i c h , i n Schoenberg's s c o r e , frames a " f o u r t h c h o r d " , A - D - G. The f u n c t i o n o f t h i s c h o r d may be shown t o p a r a l l e l t h a t o f a major-minor s e v e n t h c h o r d on A. Example 2.18 quotes t h e passage i n q u e s t i o n and p r o v i d e s a s i m p l i f i c a t i o n t h e r e o f . 3 5 Example 2.18s Opus 14, Number 1, measures 1-3 Langsam (J) Ich darf nicfat 1 p mi i r i i ' i T— ^ t|» f The f i r s t t r a d i t i o n a l progression with which the pas-sage i n Example 2.18 has harmonic voices i n common suggests a turn from the dominant of a major key to that of i t s r e l a t i v e minor; Example 2 . 1 9 shows the t r a d i t i o n a l progres-sion and Example 2.20 the harmonic voices which i t shares with the opening of Opus 14, Number 1 . Example 2 . 1 9 s F i r s t progression suggested, measures 1 - 3 -B: V 7/y..__Y 7 — y 7 — V 7 — v 7 - — I or i III III 36 Example 2.20: rb—1 - i I I 1 I I 1 1 2 A: — ' J ! h-—/ 1 1 — > -\ B: V 7 / V - — V 7 — - V 7 — V 7 — V 7 1 I I I I I I D u r i n g t h e a c t u a l l i s t e n i n g p r o c e s s , Example 2.20 p r e -cedes Example 2 . 1 9 : our t o n a l e x p e c t a t i o n s cause us t o f o c u s upon c e r t a i n harmonic v o i c e s i n the mu s i c , and th e n we are moved t o d i s c o v e r i n what c o n t e x t t h o s e v o i c e s have become f a m i l i a r . The t h r e e - c h o r d c a d e n t i a l approach t o B, " V 7 / m -V 7 - I o r i " , i s c l e a r l y i m p l i e d by the c o n v e r g i n g p a i r o f h a r -monic v o i c e s b e g i n n i n g w i t h t h e m i n o r s e v e n t h , A - G . A s s o c i -a t i n g t h e c h r o m a t i c d e s c e n t from G-sharp t o G i n the upper v o i c e w i t h m o t i o n a l o n g t h e c y c l e o f f i f t h s y i e l d s the f u n c -t i o n , V 7 / v i n D, which completes Example 2 . 1 9 . Example 2 . 1 9 i s n o t meant t o be a t r a n s l a t i o n o f what we a c t u a l l y h e a r ; i t i s m e r e l y a c h a r a c t e r i s t i c t o n a l c o n t e x t i n which some o f the more c o n s p i c u o u s harmonic v o i c e s o f the opening o f Opus 14, -Number 1 c o u l d be f e l t t o p a r t i c i p a t e , and which may, somehow, u n d e r l y the e x p e r i e n c e o f measures 1 t o 3 . The same i s t r u e o f t h e second t o n a l p r o g r e s s i o n which one might r e c a l l upon h e a r i n g t h e same passage; t h i s t i m e , a d o u b l e - n e i g h b o r p a i r i s i n v o l v e d , r a t h e r t h a n a c o n v e r g i n g mi-n o r s e v e n t h . The complete p r o g r e s s i o n i s shown i n Example 2.21, and the harmonic v o i c e s from which i t i s i n f e r r e d i n Example 37 2 . 2 2 . 1 - 3 . Example 2 . 2 1 : Second progression suggested, measures m i t , B: I r  " "I ' . - i v 7 — T S ( v I ) - V , iv7-TS(y2)-V 1 or i V V Example 2 . 2 2 : (Pitches actually present) rfJ) , i 1 \ 1 1 ^ = = ; " * 4* ^ j / - -s 1 = F = • V — — " 1 , In t h i s case, we interpret the function of the f i r s t chord of measure 1, V 7 / i v i n B, from i t s t r i t o n e , A - D-sharp. We i n f e r the resolution to i v when G appears i n measure 2, even though E-natural i s missed and we immediately hear the aug-mented version of the sixth, G - E-sharp, which characterizes the TS(V 7/V) function i n B. We hear the resolution of t h i s double-neighbor pair to F-sharp i n measure 3 when G disappears. Combining the harmonic voices of Examples 2 .20 and 2 .22 y i e l d s the esse n t i a l content of the f i r s t three measures of 38 " I c h d a r f n i c h t dankend" (Example 2.23)1 c o m p l e t i n g t h e case which has been made, t h r o u g h Examples 2.19 t o 2.22, f o r t h e p o w e r f u l i n f l u e n c e which f a m i l i a r v o i c e - l e a d i n g p a t t e r n s ex-e r t on t h e l i s t e n i n g e x p e r i e n c e . Example 2.23: E s s e n t i a l c o n t e n t o f measures l-O • Jt 1 1 . 1 I to \i 4| #1 J?i- \ Examples 2.19 and 2.20 a l s o made a case f o r t h i n k i n g o f t h e " f o u r t h c h o r d " , A - D - G, as V 7 / l I I i n B, t h e f u n c t i o n which we would n o r m a l l y a t t r i b u t e t o t h e s e v e n t h c h o r d , A - C-s h a r p - E - G. A l t h o u g h Schoenberg d i d use t h e term, " f o u r t h c h o r d " , some o f h i s examples from t h e H a r m o n i e l e h r e r e v e a l t h a t he, t o o , thought o f such s t r u c t u r e s as p o t e n t i a l s e v e n t h 3 and d o u b l e - n e i g h b o r c h o r d s . Example 2.24: (Arrows have been added t o Schoenberg's examples t o show t h e p r o g r e s s o f minor s e v e n t h s and doub l e -n e i g h b o r p a i r s . ) 332 —1 - - y b b K t o £ _ _ » ? L » 1 _ o r " —«.» : 0 " l i " i ^ L [ ^»y~r \, 1 — ^ 7 ^ — " — < > — —->o Pr-O n—— _ o —^-b-po o r ^t>x$ ~™ W * F - ^ = 39 The g e n e r a l p r i n c i p l e s i n Example 2.24 a r e t h a t a dou-b l e - n e i g h b o r p a i r e m b e l l i s h e s t h e r o o t o r f i f t h o f a t r i a d , and t h a t a minor s e v e n t h converges c h r o m a t i c a l l y ( i f n o t p a r -t i c i p a t i n g i n a " v i i 7 " - I p r o g r e s s i o n such as b e g i n s t h e ex-ample). I n Opus 15» f o u r t h c h o r ds whose d o u b l e - n e i g h b o r p a i r s e m b e l l i s h t h e r o o t s o r f i f t h s o f major and minor t r i a d s a r e p a r t i c u l a r l y i m p o r t a n t } t h e g e n e r a l i z a t i o n may be made t h a t such c h o r d s o f t e n s u g g e s t t h e f u n c t i o n s T S ( V 7 ) and T S ( V 7 / V ) , r e s p e c t i v e l y , as the f o u r t h chords s h a r e common d o u b l e - n e i g h -b o r p a i r s w i t h t h e t e r t i a n c h o r d s h a v i n g t h o s e f u n c t i o n s . F u r t h e r examples from t h e H a r m o n i e l e h r e o i n v o l v i n g l a r g e r c h o r ds c o n s i s t i n g o f t h r e e s t a c k e d p e r f e c t f o u r t h s r a -t h e r t h a n two, d i s p l a y some p o s s i b l e harmonic v o i c e m o t i o n s to and from f o u r t h chords which r e i n f o r c e t h e i d e a t h a t a d o u b l e - n e i g h b o r p a i r ( o r a minor s e v e n t h ) can, o f i t s e l f , s u g g e s t a harmonic f u n c t i o n i n t h e absence o f t h e t r i t o n e / • x 4 which would d e f i n e t h a t f u n c t i o n (Example 2.25). I n Example 2.25, arrows have been added t o Schoenberg's examples which l e a d to and from t h e d o u b l e - n e i g h b o r p a i r s o r minor s e v e n t h s which a r e r e s p o n s i b l e f o r t h e s u g g e s t e d h a r -monic f u n c t i o n s below c e r t a i n c h o r d s . Even i n such b r i e f c o n t e x t s as t h e s e , i t i s a p p a r e n t t h a t where a d o u b l e - n e i g h -b o r p a i r r e s o l v e s t o t h e r o o t o f a major o r minor t r i a d , a l o c a l T S ( V 7 ) f u n c t i o n may be i n f e r r e d (Schoenberg's examples 333a and b, and 33^). I n a d d i t i o n , a TS(V 7 / v ) f u n c t i o n c o u l d be s u g g e s t e d where the o b j e c t o f t h e d o u b l e - n e i g h b o r embel-l i s h m e n t i s t h e f i f t h o f t h e f o l l o w i n g c h o r d (Schoenberg's 40 Example 2 . 2 5 * ( from Schoenberg) a) b) C) v7' ? i ( D ) A 'P# r o o t r o o t 334 ~7L "' 7 ~rti'5 y — 1 , M i ! —V* ""55 (g j yjf -TS ( v ' O - i v' T'J TS(v' (V7)?_ ?A>? I example 3 3 3 c ) . Where t h e r e i s no d o u b l e - n e i g h b o r r e s o l u t i o n , the m inor s e v e n t h can i m p l y a l o c a l dominant f u n c t i o n i n r e -l a t i o n t o the f o l l o w i n g c h o r d (when t h e upper member o f t h e se v e n t h f a l l s b u t t h e l o w e r r e m a i n s , as i n Schoenberg's exam-p l e 3 3 3 d , f i r s t measure), o r h i n t a t a r o o t p r o g r e s s i o n down a minor t h i r d (when the s e v e n t h converges c h r o m a t i c a l l y as i n Schoenberg's example 333<*» second measure). The use o f t h e symbol "TS" t o d e s c r i b e t h e f u n c t i o n o f a c h o r d which c o n t a i n s no t r i t o n e may, a t f i r s t , seem p r o b l e m a t i c ; however, e x a m i n a t i o n o f a h y p o t h e t i c a l , two-v o i c e d p r o g r e s s i o n such as i s p r e s e n t e d i n Example 2.26 v e r i -f i e s t h a t d o u b l e - n e i g h b o r p a i r s and minor s e v e n t h s can c o n j u r e up t h e same harmonic images as do t r i t o n e s , i n a d d i t i o n t o 41 specifying whether the o r i g i n a l root of the suggested harmonic function i s present, or i t s tr i t o n e - s u h s t i t u t e . This j u s t i f i e s the use of symbols such as TS(V 7) and TS(V 7/ V) to describe the functions of certa i n fourth chords. Example 2.26: [Note minor sevenths/double neighbors and tritones at points (X).] A fourth chord which suggests the function TS(V 7 /v) i n F-sharp i s found i n measure 5 of Opus lk, Number 1. Rein-f o r c i n g such an interpretation of the chord, which consists of the pitches D, G, and C from the piano, with A from the vocal l i n e , i s the f a c t that a t e r t i a n version of the same harmonic function, TS(V 7/ V),' d i r e c t l y follows it-(Example 2.27) Example 2.27: Opus 14, Number 1, measures 5-8 42 Example 2.27» c o n t i n u e d . F#: T S ( V 7 A ) V 7 — T S ( V 7 ) r - I ( d i s c o u n t i n g CD) Example 2.28: T r a d i t i o n a l p r o g r e s s i o n r e s e m b l i n g 2.27. / r i ' " " ~ 0 : — J l - J tf * K 4 I  S ^ 7 ^ J5r*= F#: T S ( V 7 A ) V 7 1 Example 2.28 shows the t r a d i t i o n a l p r o g r e s s i o n which Example 2.27 r e s e m b l e s . The g r e a t e r c o m p l e x i t y o f the l a t t e r i s i n p a r t t h e r e s u l t o f the t w o - f o l d f u n c t i o n o f the p i t c h e s C-sharp and B i n measure 6, a l r e a d y mentioned d u r i n g t h e d i s -c u s s i o n o f d o u b l e - n e i g h b o r p a i r s i n whole-tone c o n t e x t s . Two s t a v e s have been used i n Example 2.27 t o show b o t h f u n c t i o n s c l e a r l y : t h e uppermost s t a f f shows the c o n v e n t i o n a l b e h a v i o r of C-sharp and B as a minor seventh, with B descending to A and C-sharp remaining; the lowest s t a f f shows the double-neighbor function, with the resolution of both C-sharp and B to C-natural i n measure 7. The important double-neighbor p a i r i n t h i s passage, however, i s D - C. It appears i n both the "fourth-chord" and "whole-tone" versions of TS(V?/v), and i s responsible f o r determining t h e i r single function (Example 2.29). Example 2.29s "Fourth" and "Whole-tone" versions of TS(V7/V). • « 1 I The same function, TS(V''/V)» i s made more e x p l i c i t i n the s i m i l a r passage which occurs l a t e r i n the song, shown i n Example 2.30. In t h i s case, the double-neighbor pair, D -C, immediately reaches i t s goal of C-sharp i n measure 20. Example 2.30: Opus 14, Number 1, measures 19-22. The t o n i c ^ c h o r d which a r r i v e s a t t h a t time r e s o l v e s t o t h e e x p e c t e d V 7 a l m o s t c o n v e n t i o n a l l y ; however, t h e t h i r d o f t h e dominant-seventh c h o r d , E - s h a r p , i s m i s s i n g as a r e s u l t o f t h e t r a n s p o s i t i o n o f t h e m o t i v e from measure 6 (Example 2.31) up a whole tone (Example 2.32). Example 2.31: Of course", t h i s does n o t change the harmonic f u n c t i o n o f t h e m o t i v e , V i n F-sharp, s i n c e , a t e i t h e r t r a n s p o s i t i o n , i t i s p a r t o f the same whole-tone c o l l e c t i o n ( C - s h a r p , D-s h a r p , E - s h a r p , G, A, and B ) . The t r a n s p o s i t i o n does, how-e v e r , r e s u l t i n a new, l o c a l d o u b l e - n e i g h b o r r e l a t i o n s h i p . The p a i r , C-sharp - D - s h a r p , now e m b e l l i s h e s D - n a t u r a l where B - C-sharp f o r m e r l y e m b e l l i s h e d C - n a t u r a l . These two double-n e i g h b o r e m b e l l i s h m e n t s form a l o n g - r a n g e m a n i f e s t a t i o n o f the d o u b l e - n e i g h b o r p a i r , D - C, and i t s g o a l o f C-sharp, as d e p i c t e d i n Example 2.33. Example 2.32: 45 Example 2.33* Long-range m a n i f e s t a t i o n o f the d o u b l e -n e i g h b o r p a i r , D - C I f d o u b l e - n e i g h b o r p a i r s and minor s e v e n t h s a r e impor-t a n t i n l o c a l c h o r d c o n n e c t i o n s , t h e y are i n d i s p e n s a b l e i n the c o n n e c t i o n o f key a r e a s . Two s p e c i f i c i n t e r v a l l i c r e l a t i o n -s h i p s between k e y s , which d i r e c t l y depend upon the d o u b l e -n e i g h b o r / m i n o r s e v e n t h dichotomy, are c o n s p i c u o u s i n Opus 15 and e a r l i e r songs t t h o s e o f t h e minor t h i r d and minor second. D i s c u s s i o n o f t h e s e r e l a t i o n s h i p s w i l l be the f i n a l c o n c e r n o f t h i s c h a p t e r . The M i n o r T h i r d - R e l a t i o n s h i p Schoenberg's p r a c t i c e o f h i n t i n g a t two, t h r e e , o r a l l f o u r k eys whose t o n i c s t r a c e o ut a d i m i n i s h e d - s e v e n t h c h o r d h i n g e s around the r e l a t i o n s h i p between the dominant-sevenths o f t h o s e k e y s . The m o t i o n o f harmonic v o i c e s w i t h i n any p a i r o f dominant-seventh chords i n such a complex o f f o u r i s o f two b a s i c t y p e s : ( i ) t h a t between a d j a c e n t dominant-seventh chords a l o n g the " m i n o r - t h i r d l a d d e r " , which i n v o l v e s m o t i o n from a minor s e v e n t h (major second) t o a minor s i x t h (major t h i r d ) and v i c e v e r s a (Example 2.34); and ( i i ) t h a t between n o n - a d j a c e n t dominant-sevenths i n t h e sequence o f minor t h i r d s , o r t h o s e which a r e t r i t o n e -r e l a t e d , which would i n v o l v e m o t i o n from a p e r f e c t f i f t h ( f o u r t h ) t o a p e r f e c t f o u r t h ( f i f t h )(Example 2.35). Example 2.34s M o t i o n between a d j a c e n t dominant-s e v e n t h c h ords a l o n g t h e " m i n o r - t h i r d l a d d e r " Example 2.35: M o t i o n between t r i t o n e - r e l a t e d dominant-s e v e n t h c h ords V 47 Going on the p r i n c i p l e that the tritone and the minor seventh (with i t s p o t e n t i a l to he a double-neighbor p a i r ) are the c r u c i a l i n t e r v a l s , at l e a s t one of which should be pres-ent i n a chord f o r i t to suggest some harmonic function along a cycle of f i f t h s i n a highly chromatic context, the harmonic voice motions i n Example 2.34 must be considered f u n c t i o n a l l y much more s i g n i f i c a n t than those i n Example 2.35. In the case of the l a t t e r , there i s a common tri t o n e between members of each dominant-seventh pair, and the p o s s i b i l i t y exists f o r the root and seventh of one dominant chord to act as the dou-ble-neighbor p a i r to the tonic of the other. Both of these factors, which together form the essence of the tritone-sub-s t i t u t e r e l a t i o n s h i p , make the strong implication of a change of harmonic function simply through the voice-leading i n Ex-ample 2.35 an u n l i k e l y event. Of course, where both of the tonics corresponding to a t r i t o n e - r e l a t e d dominant-seventh p a i r are suggested, two separate V' functions may emerge des-p i t e the common tritone between them. An important example of the minor-third relat i o n s h i p , which involves three of the four possible dominant-seventh chords and t h e i r respective tonics, i s found i n Opus 6, Num-ber 2, " A l l e s " . The main tonal center of the piece i s A - f l a t (with strong minor i n f l e c t i o n s ) , but emphasis upon C - f l a t and F as subsidiary centers i s clear. By measure 14, a l l three of these tonics have emerged, as revealed i n Example 2.36. In summary, measures 1 to 6 are concerned with the A-f l a t center, measures 7 to 11 with a mixture of A - f l a t and C-f l a t , and measures 12 to 14 with F. 48 Example 2 . 3 6 5 Opus 6 , Number 2 , measures 1-14. Gesang Klavier • Lass uns Doch die fait die Han - de_ in den har - ten Stei gen durch den JWI>JLTO|>JLPI!!-49 Example 2.36, continued. Harmonic voice summary of measures 1-14. do Ju 1 i 1 4 W k*- 4-1 U 1 1) . Jn> , = •I 7 0 — '1 , 1 0 1: 1 J V 1' ^ ( H b ^ f c F . 11 + \ 14 | / ^ r - ^ " ' 5 _T Y 1 : The most s t r i k i n g of the minor-third relationships i n " A l l e s " i s that between the A - f l a t and C - f l a t key areas. The f i r s t h i n t of C - f l a t occurs at the end of measure 6, where a progression from i i to V 7 i n that key i s heard; however, with the beginning of measure 7% a s h i f t back to V of A - f l a t i s i n i t i a t e d , causing confusion as i t clashes with motion be-tween V and I i n C - f l a t which i s t r y i n g to proceed simultane-ously. The two voice-leading patterns being p i t t e d against one another are shown i n Example 2.37* Although the c o n f l i c t between C - f l a t and A - f l a t i s most obvious i n measures 7 and 8, where the dominant-seventh chords of those keys are actually stated simultaneously, i t i s continued u n t i l measure 12 through foreground subtleties which are not v i s i b l e i n Example 2.36. In measure 9. for i n -stance, a progression from i i 7 to V 7 i n C - f l a t i s suggested, but where the resolution to I should occur (at the beginning of measure 10), a turn to B - f l a t minor, or i i i n A - f l a t , takes place (Example 2.38). Even during measure 10, where a return to A - f l a t through i t s i i 7 and V 7 seems imminent, pre-dominant and dominant functions i n C - f l a t are perceived i n the foreground (Example 2.39). F i n a l l y , i n measure 11, where A-f l a t re-emerges, C - f l a t also appears b r i e f l y before i t s domi-nant-seventh chord leads to V 7 of F by the tritone-substitute r e l a t i o n s h i p (Example 2.40). Though Examples 2.36 to 2.40,from Opus 6, Number 2, concerned references made to three minor-third-related tonics, Example 2.37* Clashing voice-leadings i n measure 7. \ 52 Example 2 .39s Pre-dominant and dominant f u n c t i o n s i n C - f l a t i n measure 10 . geht das Heim - wen 10 C - f l a t J Example 2.40: B r i e f appearance o f C - f l a t i n measure 11. auf den Zehn JihlSpJ?^  J H -I and V 7 i n C - f l a t . I V 53 the introduction of dominant-seventh chords i n a minor-third sequence could serve other musical purposes. One such pur-pose would be to prolong either or both of two diminished-seventh chords: type ( i ) i s that which would function as o7 v i i i n any of the four pot e n t i a l tonic keys suggested by the dominant-seventh chords, and type ( i i ) i s that a semi-tone lower, which i s traced out by the roots of the four dom-inants. A clear example of prolongation of a type ( i ) dimin-ished-seventh chord i s found i n Opus 12, Number 1, "Jane Grey". At the same place, a l e s s persuasive case might even be made for the prolongation of the corresponding type ( i i ) chord. The passage i n question, which begins with the l a s t h a l f of measure 32 and continues to measure 42, i s the bridge to and statement of the fourth verse of the ballade (Example 2.42). For the sake of t h i s discussion, l e t i t be accepted that the t o n a l i t y of "Jane Grey" i s a mixture of D and D - f l a t / C-sharp (which w i l l be elaborated upon i n the next section of t h i s chapter). From the beginning of the passage u n t i l measure 36, the diminished-seventh chord shown as Example 2.41, Example 2.41: i s prolonged i n the piano treble; i t w i l l be referred to sim-ply as ( i ) . The chord which w i l l be c a l l e d ( i i ) i s formed i n the piano bass by the alternating roots of four dominant-54 Ex-ample 2.42-; Opus 12, Number 1, measures 32-42. 55 seventh-minor-ninth chords, i n which ( i ) would serve as the four upper members (Example 2.4-3). Example 2.43s mm The long-range function of ( i ) can be shown to be vii° 7 i n D; however, more l o c a l l y , i t works with C and F-sharp from ( i i ) to form V 7 and TS(V 7) chords i n F, which resolve to i i n measure 36, as shown i n Example 2.44. I t i s only i n measure Example 2.44s . n . ^ ~ - _-' 32 =e*4 33 5*? •—b* t& i i \<=*= Fs V 7 and TS(V 7) i 42 that D appears as the tonic and the implications of ( i ) as i t s v i i 0 7 are r e a l i z e d . Preventing a d i r e c t connection between ( i ) and the ton-i c i n measure 42 are measures 37 to 41, which are completely concerned with harmonic functions i n C-sharp/D-flat, rather than D. Measures 37 and 38 introduce V 7 of D-flat and hint 7 7 at the r e l a t i v e key, B - f l a t , with the progression, i i f to V of v i (Example 2.45); measures 29 to 41 (second beat) proceed 56 through a very t r a d i t i o n a l preparation of and a r r i v a l at a cadential 1^ i n D-flat (Example 2.46) which, however, goes astray and leads to a novel combination of dominant elements i n both D - f l a t and D by the end of measure 41. The harmonic Example 2.45: Opus 12, Number 1, measures 36-38. i i 7 - V 7 V7 of v i 57 Example 2.46: Opus 12, Number 1, measures 39-42. s t r u c t u r e a t ( x ) i n Example 2.46 c o n t a i n s t h r e e p i t c h e s o f vii° 7 i n D - f l a t ( E - f l a t , G - f l a t , and A, o r B - d o u b l e - f l a t ) ; i f C - n a t u r a l were s u b s t i t u t e d f o r C-sharp as t h e f o u r t h mem-be r o f t h i s s t r u c t u r e , a c o n v e n t i o n a l r e s o l u t i o n t o I i n D-f l a t c o u l d t a k e p l a c e o v e r the b a r - l i n e to measure 42. How-e v e r , t h r e e o f t h e p i t c h e s a t (x) su g g e s t a dominant f u n c -t i o n i n Dt C-sharp, E - f l a t , and A. The d o u b l e - n e i g h b o r p a i r , C-sharp - E - f l a t , i s c h a r a c t e r i s t i c o f T S ( V 7 ) , and A, o f c o u r s e , i s t h e dominant p i t c h o f D; t h e s e t h r e e p i t c h e s a r e r e s p o n s i b l e f o r the sudden, and somewhat u n c o n v i n c i n g , r e s o l u t i o n o f t h e (x) c h o r d t o i i n D. The r e s o l u t i o n t o D i n measure 42 does n o t a l l o w one t o f o r g e t t h e s t r o n g harmonic f u n c t i o n s i n D - f l a t which oc-58 c u p i e d measures 37 t o 41, n o r does i t answer the q u e s t i o n o f how the D - f l a t passage r e l a t e s t o chords ( i ) and ( i i ) o f measures 32 t o 36. Examples 2.44 and 2.45 showed how ( i ) l e d t o an F m i n or c h o r d , o r i i i i n D - f l a t ; the same examples r e v e a l something more s u b t l e about ( i i ) , w i t h r e s p e c t t o D-f l a t . When V 7 o f D - f l a t i s i n t r o d u c e d i n measure 37, we r e -c o g n i z e t h a t i t s t r i t o n e , C - G - f l a t , has been p r e s e n t s i n c e measure 32, i n the form o f a l t e r n a t i n g r o o t s t o c h o r d ( i ) , C and F-sharp; th e p o s s i b i l i t y o f i n t e r p r e t i n g ( i i ) as a sub-t l e h i n t o f vii° 7 i n D - f l a t , d e s p i t e i t s l i n e a r d i s p o s i t i o n o v e r measures 32 t o 36, must be a l l o w e d , i n v i e w o f the ob-v i o u s harmonic v o i c e c o n n e c t i o n s between C and D - f l a t , and G - f l a t and F. Example 2.47 d e p i c t s what was r e f e r r e d t o on page 53 as t h e " l e s s p e r s u a s i v e c a s e . . . f o r t h e p r o l o n g a t i o n O 7 o f . . . ( i i ) " (as v i i ' o f D - f l a t ) a l o n g w i t h t h e l o n g - r a n g e f u n c t i o n o f ( i ) as v i i 0 7 o f D. o7 Example 2.47: Long-range v i i ' f u n c t i o n s i n D and D - f l a t . Ds v i i ' (x) i I n summary, the passage from "Jane Grey" may be s a i d 59 t o emphasize t h e l i n k between f o u r m i n o r - t h i r d - r e l a t e d major-m i n o r - s e v e n t h chords» t h e p r e s e n c e o f t h e upper t h r e e mem-be r s o f each i n a common d i m i n i s h e d - s e v e n t h c h o r d , c h o r d ( i ) . T h i s l i n k e n a b l e d t h e f o u r c h o r d s t o be used t o e x p r e s s t h e o7 s i n g l e f u n c t i o n , v i i ' i n D. The passage from " A l l e s " , d i s -c u s s e d p r e v i o u s l y , emphasized t h e i n d i v i d u a l dominant-seventh f u n c t i o n s o f t h r e e m i n o r - t h i r d - r e l a t e d chords by t h e appear-ances o f t h e i r r e s p e c t i v e t o n i c s . Through t h e two pa s s a g e s , examples o f b o t h t h e c o l l e c t i v e and s e p a r a t e f u n c t i o n i n g o f m a j o r - m i n o r - s e v e n t h chords i n a m i n o r - t h i r d sequence a r e r e -v e a l e d . The Minor-Second R e l a t i o n s h i p " ^ Schoenberg c o n n e c t s s e m i t o n a l l y - r e l a t e d k e y s by means o f two b a s i c t y p e s o f harmonic d o u b l e i n t e r p r e t a t i o n . The f i r s t r e l i e s upon t h e i d e n t i t y between V 7 o f a g i v e n k e y and TS(V 7/V) o f t h a t a semi-tone l o w e r , and i t s c o r o l l a r y , the e q u a l i t y o f V 7/V i n t h e l o w e r key t o T S ( V 7 ) i n t h e upper. Example 2.48t T h i s t y p e o f double i n t e r p r e t a t i o n con-t r a s t s t h e d o u b l e - n e i g h b o r and m i n o r - s e v e n t h f u n c t i o n s o f en-h a r m o n i c a l l y e q u i v a l e n t c h o r d s . _D~* V ^ = ' I C#TTS _("^—J^I DTTS~(T 7)^lC D J ? : ^ « V 7 The second t y p e i n v o l v e s t h e i n t e r p r e t a t i o n o f a g i v e n aug-mented t r i a d as I#5 i n the l o w e r key, and e i t h e r as V#5 o r i w i t h suspended l e a d i n g - t o n e i n t h e upper (Example 2.49). C h a r a c t e r i s t i c o f t h e mi n o r - s e c o n d r e l a t i o n s h i p i n 60 Example 2.4-9« Double i n t e r p r e t a t i o n o f an augmented t r i a d . C#s I#5 Ds V#5 o r i Schoenberg's music i s t h a t elements o f f u n c t i o n a l harmony i n b o t h keys appear a l t e r n a t e l y , and even p r o c e e d s i m u l t a n e o u s l y , y e t a g e n e r a l Roman numeral a n a l y s i s f r e q u e n t l y can be done which a c t u a l l y o v e r l o o k s t h e f a c t t h a t two keys a r e b e i n g im-p l i e d and s t i l l makes t o n a l s e n s e . T h i s t e s t i f i e s t o t h e as-t o u n d i n g degree o f i n t e g r a t i o n between the two k e y s which Schoenberg a c h i e v e s . The work which d e p i c t s most s t r i k i n g l y t h e m i n o r - s e c -ond r e l a t i o n s h i p , a c c o m p l i s h e d t h r o u g h t h e two t y p e s o f dou-b l e i n t e r p r e t a t i o n j u s t i n t r o d u c e d , i s Opus 12. Both songs, "Jane Grey" and "Der v e r l o r e n e Haufen", a r e ba s e d upon t h e m i n o r - s e c o n d - r e l a t e d t o n i c p a i r , D - C - s h a r p / D - f l a t . I n each song, D i s t h e i n i t i a l and f i n a l t o n i c , b u t s u b s t a n t i a l p a s s a g -es a r e b e s t i n t e r p r e t e d i n C-sharp o r D - f l a t i a d d i t i o n a l t o n i c s a r e h i n t e d a t by t h e m i n o r - t h i r d r e l a t i o n s h i p between domi-n a n t - s e v e n t h c h o r d s d i s c u s s e d i n t h e p r e c e d i n g s e c t i o n o f t h i s c h a p t e r . The i m p o r t a n t keys i n "Jane Grey" may be diagrammed t h u s t D_ ( F ) (B>)- pi ( T h i s s k e t c h does n o t r e p r e s e n t an o r d e r o f o c c u r r e n c e , s i n c e 61 the tonics fade i n and out; i t i s only meant to show the main minor-second and subsidiary minor-third relationships.) Measures k to 1 2 of "Jane Grey" w i l l be dealt with i n t h i s regard. Example 2 . 5 0 » Opus 1 2 , Number 1 , "Jane Grey", meas-ures k to 1 2 . n Hof, daB ihm seui Spriich ge Sie fiihr - ten Urn durch den grau - eni - g b r -i i Grey. ' espress. ¥ f ^ r F ^ ^ r " ^4 u ' q — r f f c - 1 ^ espress. Measures 5 to 1 2 , i n c l u s i v e , to which the f i r s t stan-za of poetry i s set, contain elements of a l l four of the keys i n the aforementioned diagram (page 6 0 ) . The simple, two-times-two-measure structure of the passage harbours a correspondingly simply harmonic scheme, barring the f a c t that one's point of tonal reference subtly s h i f t s from D 62 to F, then D- f l a t , and f i n a l l y , B - f l a t , i n the course of eight measures of music. Example 2.51 shows the harmonic scheme of measures 4 to 12; the tonic(s) to which each Roman numeral applies may change, but i t must be emphasized that the passage, as a whole, creates the same basic e f f e c t , i n terms of musical "rhetoric", as i t would i f the harmonic scheme were applied to a single tonic. Example 2.51: Dots (...) indicate that a given tonic i s i n e f f e c t . Note the mixture of D and D - f l a t at measure 8. Measure: 4— - , 5 — 6—, 7—8—-, 9—10—, 11—12—, Function: h l - V 7 , i — V 7 - - , I — V — , I - I V - i i - , l £ - v 7 - I — , (F : ) (D i ) (D>« ) (B>i ) A sketch of the harmonic voices i n measures k to 12 which c l a r i f i e s the roles of the two most important tonics, D and D - f l a t , i s given i n Example 2.52, page 63. We can describe t h i s passage from "Jane Grey" subjec-t i v e l y , i n terms of general musical gestures and correspond-ing, t r a d i t i o n a l progressions which would be found i n a harmonically simpler, but s i m i l a r l y structured stanza of a song. F i r s t , measure 4 ends the introduction with a very fam-i l i a r approach to the D minor tonic: the progression from (or the "Neapolitan-sixth" chord) to V 7. Then, there i s a four-measure antecedent phrase (measures 5 to 8), followed by a balancing consequent phrase (measures 9 to 12). Both phras-63 Example 2.52» Harmonic v o i c e s k e t c h o f measures 4 t o 12 o f "Jane Grey". The upper system r e l a t e s t o t h e t o n i c s D and F, and t h e l o w e r system t o D - f l a t and B - f l a t . Square b r a c k e t s show how t h e music c o r r e s p o n d s t o t h e i n d i v i d u a l l i n e s o f p o e t r y . T — i i 7 — ( V ? ) —I#5-iv 7-ii 7-TS B^t (v#5?) (^5-it" (no D3) i i ' - V I es may be h a l v e d , r e s u l t i n g i n f o u r two-measure groupss 5-6, 7-8, 9-10, and 11-12. The f i r s t h a l f o f t h e a n t e c e d e n t p h r a s e might be de-s c r i b e d as t h e t e n t a t i v e d e p a r t u r e from t h e t o n i c , and t h e second h a l f as t h e d e c i s i v e d e p a r t u r e , t h e l a t t e r e n d i n g i n a semi-cadence. A s i m p l e , p r o t o t y p i c a l a n t e c e d e n t p h r a s e which c a p t u r e s t h e essence o f t h e harmonic e v e n t s i n meas-u r e s 5 t o 8 w h i l e s t a y i n g w i t h i n one t o n i c key i s g i v e n - i n Example 2.53; a s l i g h t l y more complex p h r a s e which comes c l o s e r t o t h e a c t u a l e v e n t s i n "Jane Grey" by i n c l u d i n g a 64 h i n t o f t h e r e l a t i v e major key i n i t s second measure appears i n Example 2.54. Example 2.53' H y p o t h e t i c a l , s i m p l e r a n t e c e d e n t p h r a s e , analogous t o measures 5 t o 8 o f "Jane Grey", b u t which r e -mains i n D mi n o r . D: i - — V I i i ' V i____XZ 1 V V' Example 2.54« More complex p h r a s e , i n c l u d i n g elements which s u g g e s t F major, as i n "Jane Grey" i n measure 6. -D-i—i—- -V I — -V7/V—.-y 7 F Comparison o f Example 2.54 w i t h t h e c o r r e s p o n d i n g p o r -t i o n o f Example 2.52 on page 63 r e v e a l s t h e o n l y s i g n i f i c a n t d i f f e r e n c e between t h e two; i t i s t h a t D - f l a t r a t h e r t h a n D appears where t h e t o n i c i s supposed t o r e t u r n i n p r e p a r a t i o n f o r t h e semi-cadence ( a t t h e b e g i n n i n g o f measure 7) i n t h e e a r l i e r example. Example 2.52 a l s o shows t h a t t h e dominant i n measure 8 i s i n t e r p r e t a b l e i n b o t h D - f l a t and D r W i t h r e s -p e c t t o D - f l a t , t h e l e a d i n g - t o n e , C, i s emphasized, h a v i n g been p r e p a r e d i n measure 7 by t h e p r o g r e s s i o n from I t o i i 7 i n D - f l a t , w hich made D - f l a t t h e d i s s o n a n t s e v e n t h ; i n a d d i -t i o n , measure 8 c o n t a i n s i m p l i c a t i o n s o f t h e dominant o f D, 65 i n t h e form o f t h e p i t c h e s A, C-sharp, and E. F u r t h e r e l e -ments which add to the sense o f a dominant f u n c t i o n i n D are the B - f l a t ( p r e s e n t i n v i i 0 7 o f D) and the F/E-sharp ( p r e s e n t i n V#5) f o u n d i n t h e p i a n o t r e b l e i n measure 8. The r e s o l u t i o n to the D - f l a t augmented t r i a d i n meas-ur e 9 may be seen as a compromise between "pure" r e s o l u t i o n s i n D - f l a t m a jor and D minor which might have t a k e n p l a c e as shown i n i x a m p l e s 2.55 and 2.56, r e s p e c t i v e l y . Example 2.55' H y p o t h e t i c a l r e s o l u t i o n t o D - f l a t m a j o r . ! • 5 i V ? — l j ? p J 1 1 ' 'V 1 i I I I I ft - ^ r r (8)' [ \ 1 (< -h ' 1 UrU Example 2.56« H y p o t h e t i c a l r e s o l u t i o n t o D minor. 66 The g e n e r a l m u s i c a l g e s t u r e s i n t h e consequent p h r a s e o f measures 9 t o 12 a r e c l e a r . The f i r s t h a l f o f the phrase r e p r e s e n t s a harmonic i n t e n s i f i c a t i o n which p r e p a r e s f o r t h e f i n a l and most d r a m a t i c a r r i v a l a t the dominant [ w i t h m o t i o n from t h e t o n i c to t h e subdominant, f o l l o w e d by t h e pre-^domi-n a n t f u n c t i o n s , i i 7 and T S ( V 7 / V ) ] } t h e second h a l f i n v o l v e s the f i n a l cadence i t s e l f , b e g i n n i n g t y p i c a l l y , w i t h a t o n i c ^ c h o r d which one e x p e c t s t o r e s o l v e t o V and t h e n I . To compose a s i m p l e r v e r s i o n o f t h e f i r s t h a l f o f the consequent p h r a s e , we need n o t change s i g n i f i c a n t l y t h e p r o -g r e s s i o n i n t h e p i e c e which i s shown i n Example 2.52, e x c e p t to have i t o c c u r i n D i n s t e a d o f D - f l a t , so t h a t t h e music f o l l o w s l o g i c a l l y from Example 2.54. T h i s i s done i n Exam-p l e 2.5?. Example 2.57t Harmonic p r o g r e s s i o n analogous t o t h a t i n measures 9 and 10, b u t w i t h D as t h e t o n i c i n s t e a d o f D-f l a t . D: i — 7 ? i v i i 7 — T S ( ^ £ ) . i v -' — — *V (**V7/iv has been s u b s t i t u t e d f o r the c o n t i n u e d I#5 o f 2.52) The f i n a l cadence which one would e x p e c t t o f o l l o w from Example 2.57 appears i n Example 2.58, which shows the complete, h y p o t h e t i c a l consequent p h r a s e . Comparing t h i s p h r a s e w i t h measures 9 t o 12 o f Example 2.52, we f i n d essen-t i a l l y t h e same p r o g r e s s i o n o f harmonies up t o and i n c l u d i n g 67 the f i r s t h a l f of measure 11, except that i t i s happening i n D minor rather than D-flat major i n the hypothetical phrase. In the l a s t h a l f of measure 11, a turn to B - f l a t takes place i n the o r i g i n a l music which i s omitted i n Example 2.58. Example 2.58: The hypothetical consequent phrase, which remains i n D minor (analogous to measures 9-12). X) • <5> V > # f S I l i o ) »-S-(11) -•• # -(12) o * v # — -J- ' =. 1 D: i — XL — I V I V ii 7-Ts<^)~i<;—_v? i Cadence The actual consequent phrase would he i d e n t i c a l to Example 2.58, save the substitution of D f o r D - f l a t as the tonic i n the l a t t e r , i f measure 11 of "Jane Grey" proceeded from the D - f l a t ^ chord as depicted i n Example 2.59« Example 2.59: Hypothetical close i n D - f l a t (analogous to measures 11 and 12). tee die scho - ne Ko -( I D 3 fi£ 68 Example 2.59» c o n t i n u e d Harmonic v o i c e summary o f t h e h y p o t h e t i c a l c l o s e A l t h o u g h t h e consequent p h r a s e , i n i t s o r i g i n a l form, i s c l e a r l y i n D - f l a t , a s h i f t back to, D c o u l d be a c h i e v e d s i m p l y , on two o c c a s i o n s d u r i n g measures 9 t o 12. The f i r s t i s i n measure 10, where t h e p r o g r e s s i o n f r o m i i t o TS(V?/v) i n D - f l a t b e a r s some s i m i l a r i t y t o t h a t from t o V 7 i n D which o c c u r r e d i n measure 4; t h e minor a l t e r a t i o n s o f G - f l a t t o G - n a t u r a l and C - n a t u r a l t o C-sharp i n t h e two c h o r d s , r e s -p e c t i v e l y , would e n a b l e a smooth r e s o l u t i o n t o a D minor ^ c h o r d t o t a k e / p l a c e a t t h e b e g i n n i n g o f measure 11, as shown i n Example 2.60. The second o c c a s i o n i s i n measure Example 2.60t A p o s s i b l e s h i f t back t o D minor i n measures 10 and 11. (10) If* ( I D 12, where t h e d o u b l e - n e i g h b o r p a i r , E - f l a t and C-sharp, r e -s o l v e s t o D, t h e t h i r d o f a B - f l a t major t r i a d ; t h e same 69 double-neighbor re s o l u t i o n might have been part of a progres-sion from TS(V 7) to i i n D (Example 2.61). Example 2.61J Return to D minor at the l a s t moment, i n measure 12. Of the examples dealing with t h i s passage from "Jane Grey" (2.52 to 2.60), several manifest one of the basic types of double in t e r p r e t a t i o n set out i n Examples 2.48 and 2.49 of pages 59 and 60. The former type, which r e l i e s upon the double-neighbor/minor seventh dichotomy, i s apparent i n Examples 2.59 and 2.60, which concern the equivalence be-tween V 7/v i n D - f l a t and TS(V 7) i n D; the l a t t e r type arises i n Examples 2.55 and 2.56, which deal with the equivalence between I#5 i n D - f l a t and i , with suspended leading-tone, i n D. 70 CHAPTER I I I AN ANALYSIS OF OPUS 15, NUMBER '§ The most i m p o r t a n t harmonic r e l a t i o n s h i p s i n Opus 15, Number 5 a r e summarized i n Example 3*0. T h i s example i s n o t meant t o d e p i c t t h e c h r o n o l o g i c a l o r d e r o f ev e n t s i n t h e p i e c e , b u t t o map i n a b s t r a c t f orm t h e c r u c i a l harmonic con-n e c t i o n s w h i c h c h a r a c t e r i z e t h e m u s i c . (A r e p r o d u c t i o n o f the e n t i r e p i e c e appears i n Example 3.1 , pages 71 and 72.) Example 3.0« Harmonic r e l a t i o n s h i p s i n Opus 15t Number 5* With r e g a r d t o t o n a l c e n t r e s , i t i s B and D which a r e most s t r o n g l y suggested? t h e l a t t e r n e v e r a c t u a l l y a p p e a r s , b u t i t s p r e s e n c e i s f e l t due t o c o n v i n c i n g p r e p a r a t i o n s o f i t s dominant, which f a i l s t o r e s o l v e t o D. The p i t c h e s G and B - f l a t become i m p o r t a n t when t h e harmonic f u n c t i o n s o f 71 Example 3»1« °Pus 15* Number 5. 72 Example 3»lt c o n t i n u e d . 73 TS(V 7/V) i n B and D a r e emphasized enough f o r t h e i r a l t e r -n a t e i d e n t i t i e s as m a j o r - m i n o r - s e v e n t h chords on the r o o t s G and B - f l a t t o be r e c o g n i z e d . I n t h e l a s t h a l f o f t h e p i e c e , G and B - f l a t a r e g i v e n t h e s t a t u r e o f h i n t e d t o n i c s , a l t h o u g h t h e i r main f u n c t i o n s p r ove to be as members o f t h e u n s t a b l e harmonic s t r u c t u r e s i n which t h e y appear i n Example 3 « 0 . Example 3 * 2 i s d e r i v e d from 3 . 0 , and shows the p i t c h e s which a c h i e v e some degree o f t o n i c s t a t u s d u r i n g the p i e c e . Example 3 . 2 t T o n i c s i n Opus 1 5 , Number 5 ( N o t i c e the s i m i l a r i t y between t h i s example and t h a t a t t h e bottom o f page 6 0 , which mapped the t o n a l c e n t r e s i n Opus 1 2 , Number 1 . ) G- B ^ -D The f i r s t p h r a s e o f t h e p i e c e , c o m p r i s i n g measures 1 and 2 , i n t r o d u c e s B as a t o n i c . The harmonic p r o g r e s s i o n i n t h e s e measures b e a r s o v e r t resemblance t o , and s e r v e s t h e same purpose as would, one a l o n g t h e c y c l e o f f i f t h s i n B from V ' / i i t o i . T h i s can be shown by recomposing the p h r a s e i n s e v e r a l s t a g e s , t h e f i r s t o f which i n v o l v e s s i m p l i f y i n g the v o c a l l i n e t o show i t s b a s i c d e s c e n t from F-sharp t o D, as shown i n Example 3 - 3 . I n t h e n e x t s t a g e , h a v i n g n o t i c e d t h a t t h e E and D o f .the v o c a l l i n e a r e d i s p l a c e d one c h o r d t o t h e l e f t f r o m what would be t h e p r o p e r a l i g n m e n t f o r a cadence from T S ( V 7 ) t o i i n B, we c o r r e c t t h e s i t u a t i o n (Example 3 . 4 ) . F i n a l l y , we i n t r o d u c e G-sharp as t h e r o o t o f t h e f i r s t c h o r d i n measure 1 , h a v i n g a l l o w e d i t s t r i t o n e , C/B-sharp -74 F-sharp, t o determine i t s f u n c t i o n as V 7 / i i i n B; i n a d d i -t i o n , we r e s t o r e V 7/V and V 7 t o t h e i r t r a d i t i o n a l forms. The r e s u l t i s t h e p r o t o t y p i c a l p r o g r e s s i o n shown i n Example 3»5» f i r s t i n n o t a t i o n which emphasized t h e r o o t movements, and t h e n i n harmonic v o i c e n o t a t i o n (page 75). t i o n . Example 3*3* Measures 1-2, f i r s t s t a g e o f r e c o m p o s i -Gesang Klavier Etwas langsam (J ca 66} Sa - get mir, auf wel-chem Pfa - de Di - tea moi sur quel - le rou - te H p S i r El Example 3*4* Second s t a g e o f r e c o m p o s i t i o n . B i r 7 / y — — — — T S ( V 7 ) — i 75 Example 3.5s Measures 1-2, f i n a l s t a g e o f r e c o m p o s i -t i o n , r e s u l t i n g i n a p r o g r e s s i o n a l o n g the c y c l e o f f i f t h s . F o l l o w i n g t h i s a r r i v a l a t t h e t o n i c , B, i s a p r o g r e s -s i o n t o t h e dominant o f D, which i s completed by measure 6. S i n c e the minor mode o f B r a t h e r t h a n t h e major was s u g g e s t -ed i n measures 1 and 2, t h i s p r o g r e s s i o n has the e f f e c t o f a t u r n t o the " r e l a t i v e major", even though D major, o r mi-no r , n e v e r appears. C r u c i a l t o t h e p r o g r e s s i o n t o V 7 o f D i s t h e m o t i o n from T S ( V 7 / V ) i n B t o t h e same f u n c t i o n i n D, which o c c u r s i n measures 3 and 4. A summary o f t h e s e meas-u r e s i s g i v e n i n Example 3*6. Example 3*6* Measures 3-k. 76 Example 3 . 6 , c o n t i n u e d Measures 3 -4: whole-notes a r e th o s e p r e s e n t i n t h e v o c a l l i n e . o f B o f D The c h o r d which u l t i m a t e l y f u n c t i o n s as T S ( V 7 / V ) i n D i s shown i n ( i ) and ( i i ) o f Example 3 .6 as a B - f l a t major-mi-n o r - s e v e n t h c h o r d ; t h i s n o t a t i o n i s c o n s i s t e n t w i t h t h e chord's more l o c a l f u n c t i o n , V 7 / b l I i n D. T h i s f u n c t i o n be-comes apparent w i t h t h e b e g i n n i n g o f measure 5t where |?II o f D app e a r s ; t h e s u b s t i t u t i o n o f A f o r G does n o t o b s c u r e t h e b l l f u n c t i o n , b u t r e c a l l s t h e a p p o g g i a t u r a from t h e r a i s e d f o u r t h t o t h e t h i r d o f t h e G m a j o r - m i n o r - s e v e n t h c h o r d i n measure 3t as shown i n Example 3*7• 77 Example 3.7 s "4-3" m o t i o n i n measure 3 and a s i m i l a r i n f e r e n c e i n measure 5• The c h o r d o f measure 5 marks t h e b e g i n n i n g o f a most f a m i l i a r approach t o V? o f D. Example 3*8 e x t r a c t s t h e r e l e v a n t p i t c h e s from t h e m u s i c , l e a v i n g them i n t h e i r o r i g i n a l r e g i s t e r s , w h i l e 3.9 r e a r r a n g e s t h e p i t c h e s r e g i s -t r a l l y t o y i e l d t h e same p r o g r e s s i o n i n harmonic v o i c e n o t a -t i o n . Example 3.8t Measures 5-6, approach t o V 7 o f D (Whole n o t e s i n d i c a t e which p i t c h - c l a s s e s a r e found i n t h e v o c a l l i n e . ) dafi. mes -i r h aus d e r reieh - sten L a . de se - crets trk - sors pour el - le nut znrtem Ausdruck z a r ii 78 Example 3.9« Measures 5-6 i n harmonic v o i c e n o t a t i o n . E l i m i n a t i n g the F-sharp and E - f l a t o f t h e f i r s t c h o r d i n measure 6, which may be i n t e r p r e t e d as a suspended and pas-s i n g tone,, r e s p e c t i v e l y , and o m i t t i n g t h e minor n i n t h o f V 7 o f D a l l o w s t h e p r o t o $ y p i c a l p r o g r e s s i o n o f Example 3.10 t o emerge. Example 3.10J P r o t o t y p i c a l approach to V 7 o f D . 3 T Dl' t i l V7/hl rj T S ( V 7 / V ) V' The semi-cadence from TS(V 7/V) t o V 7 i n D ends a s i x -measure passage c o n s i s t i n g o f Ithree v e r y b a s i c harmonic ges-t u r e s * (1) t h e approach and V - I cadence t o a t o n i c (measures 1 and 2); (2) t h e d e s t a b i l i z a t i o n o f t h a t t o n i c p i t c h t h r o u g h t h e i n t r o d u c t i o n o f t h e l e a d i n g - t o n e t o t h e domi-n a n t , which f o r c e s t h e t o n i c down t o i t s l e a d i n g -tone (measures 3 and 4); ( i t s h o u l d be n o t e d t h a t t h i s p r o c e s s i s u s u a l l y i n i t i a t e d t o a c h i e v e a r e -s o l u t i o n from V 7 / V t o V, as shown i n Example 3.11* 79 a l t h o u g h t h e a c t u a l s i t u a t i o n i n measures 3 and k i n v o l v e s t h e des c e n t from t h e t o n i c , B, t o B-f l a t r a t h e r t h a n A-sharp, and a p r o g r e s s i o n from TS(V7/V) i n B t o TS(V7/V) i n D, as i n Example 3 . 1 2 ) ; .Example 3 . 1 1 s ^Example 3 . 1 2 : ( 3 ) a s h i f t t o t h e dominant o f the r e l a t i v e m a jor, r e s u l t i n g i n t h e f u r t h e r descent o f t h e o r i g i n a l l e a d i n g - t o n e by a semitone t o t h e new dominant p i t c h (Example 3 . 1 3 ) . Example 3 . 1 3 : 80 The t h r e e g e s t u r e s j u s t d e s c r i b e d o c c u r i n t h r e e and f o u r harmonic v o i c e s . Of t h e s e v o i c e s , t h e ones which i n -v o l v e t h e p r o g r e s s o f t h e o r i g i n a l t o n i c p i t c h , B, a r e p a r -t i c u l a r l y i m p o r t a n t , s i n c e t h a t p i t c h was i n t r o d u c e d t o us as th e f i r s t t o n a l l y s t a b l e p o i n t i n t h e mu s i c , however f l e e t i n g -l y . The harmonic v o i c e shown by t h e beamed p i t c h e s o f Exam-p l e 3*13 r e c e i v e s t h e impetus t o descend two semitones from i t s i n i t i a l l y s t a b l e B i n the f o l l o w i n g way (Example 3.14). Example 3.14» Note the t r i t o n e s a t t h e p o i n t s ( X ) . The two t r i t o n e s , a t t h e p o i n t s ( X ) , a r e t h e s o n o r i t i e s which m o t i v a t e t h e f i r s t s i x measures o f Opus 15* Number 5» th e B - f l a t o f the beamed v o i c e i s t h e r e s u l t o f t h e f i r s t t r i -t o n e , and t h e A t h a t o f t h e second. The t r i t o n e s o c c u r w i t h -i n TS(V?/v) f u n c t i o n s i n B and D, r e s p e c t i v e l y , t h o s e f u n c ^ t i o n s h a v i n g been i n t r o d u c e d a t the o u t s e t o f t h i s d i s c u s -s i o n as fundamental t o t h e p i e c e . H a v i n g now made th e o b s e r -v a t i o n t h a t t h e s e f u n c t i o n s c o l l a b o r a t e t o b r i n g t h e o r i g i n -a l t o n i c p i t c h , B, down two s e m i t o n e s , our co n c e r n s i n t h e c o n t i n u e d d i s c u s s i o n o f t h e p i e c e must i n c l u d e a s t u d y o f how t h i s p r o c e s s i s r e v e r s e d , s i n c e , i n d e e d , we f i n d ascend-i n g c h r o m a t i c m o t i o n back t o B by t h e end o f t h e p i e c e . 81 In terms of p i t c h alone, measures 7 and 8 have essen-t i a l l y the same meaning as do measures 5 and 6 s therefore, i t may seem strange not to have included them i n the d i s -cussion of the e a r l i e r two measures. However, measures 7 and 8 play an e n t i r e l y new r o l e i n terms of musical d i s -course, i n addition to whatever e f f e c t they might have as an echo of measures 5 and 6. They i n i t i a t e a four-measure passage which diminishes the sense of semi-cadence we might f e e l at the end of measure 8. The momentum which brings i n measure 9 stems c h i e f l y from the vocal part, which i s i n mid-phrase during measure 8, having broken away from the es-tablished two-measure grouping which i s c a r r i e d on i n the accompaniment, and with which i t was synchronized i n the f i r s t s i x measures of the piece. What frees the vocal l i n e from the two-measure grouping i s the elongation of the rhythmic pattern which i t stated i n measures 1-2, 3-4, and 5-6i the s p e c i f i c r e s u l t of t h i s i s that the l i n e one ex-pects the vocal* part to complete i n measures 7 and 8 ac-t u a l l y l a s t s into measure 9» as shown i n Example 3-15* Example 3'158 Rhythmic patterns of the vocal l i n e i n measures 1-2, 3-4, 5-6, and 7-9 • 1-2: 3-4: 5-6: 7-9 s 8 2 Of course, i t i s more than the obvious one-to-one cor-respondence between the pitches of the vocal l i n e i n meas-ures 7-9 and those of the three preceding vocal phrases which j u s t i f i e s i n t e r p r e t i n g the three-measure fourth phrase as an elongated version of a two-measure phrase. The s t r i k -ing s i m i l a r i t y of melodic contour between the vocal phrases of measures 5-6 and 7-9 f o r t i f i e s such an inte r p r e t a t i o n (Example 3.16)^ as does the f a c t that the accompaniment i n measures 7^ 8 i s almost i d e n t i c a l to that i n measures 5-6. Example 3.16: Comparison of the melodic contour of the vocal phrase i n measures 5-6 with that i n 7-9* measure 7 8 9 The most convincing way of i l l u s t r a t i n g the rhythmic d i s t o r t i o n of the fourth vocal phrase, however, i s to remove i t . To have the phrase take place i n two measures rather than three, and to follow a rhythmic pattern s i m i l a r to those of the f i r s t three phrases proves fascinating; we f i n d that remarkable coincidences of pi t c h content ex i s t between the hypothetical, shorter vocal phrase and i t s accompaniment i n measures 7-8 (Example 3.I7). The two-measure version of the fourth vocal phrase n creates a d e f i n i t e semi-cadence with the a r r i v a l of V' of D 83 Example 3«17« H y p o t h e t i c a l two-measure v o c a l p h r a s e , c r e a t e d by c o m p r e s s i n g the m a t e r i a l o f measures 7-9 i n t o 7-8» c u r v e d l i n e s show p i t c h - c l a s s c o r r e s p o n d e n c e s between t h e v o c a l l i n e and t h e accompaniment. \}L j 1 Op «L-> ^ ^ — (7) J \ \ (8> l i r e -J ^ — — — / - — l \ r •f 1 ^ 1 i n measure 8, and i s e n t i r e l y c o m p a t i b l e w i t h t h e measure g r o u p i n g s o f 7-8 and 9-10 s u g g e s t e d by the m e l o d i c s t r u c t u r e o f t h e accompaniment (Example 3.18). The a c t u a l three-meas-Example 3'18s Two-measure groups i n t h e p i a n o accom-paniment. measures 7-8 measures 9-10 u r e v o c a l p h r a s e must work a g a i n s t t h e c o n t r a s t i n g two meas-ure groups o f Example 18, which a r e r e i n f o r c e d by t h e h a r -monic f u n c t i o n s i n measures 7-8 and 9-10. Measure 9 may be s a i d t o r e p r e s e n t a harmonic " c a t c h - s t e p " , which e s s e n t i a l l y r e p e a t s t h e harmonic f u n c t i o n o f measure 8 w i t h renewed pur-pose, t h e o n l y change b e i n g t h a t TS(V^) o f D r e p l a c e s the p r e -c e d i n g V?. The r e s u l t i n g sense i s o f two s u r g e s o f harmonic 84 a c t i v i t y , moving f o r w a r d as i n t h e n u m e r i c a l sequence 12 3, 3 4 5 (Example 3.19). Example 3.19* Harmonic v o i c e summary o f measures 7-10 (Note t h a t measure 10 r e p r e s e n t s the b e g i n n i n g o f a new v o c a l p h r a s e as w e l l as the end o f a two-measure group i n the accom paniment: t h e l a t t e r o f t h e s e a s p e c t s i s r e l e v e n t t o t h i s ex-85 The o u t e r v o i c e s o f t h e t h r e e chords i n measures 9 and 10 o f Example 3-19 c h a r a c t e r i z e the c o n v e n t i o n a l p r o g r e s s i o n s from a I V ^ 7 o r i i 7 c h o r d t h r o u g h TS(V 7/V) t o l£ o f B - f l a t w hich a r e shown i n Example 3*20. However, t h e a c t u a l p r o -Example 3'20J P r o t o t y p i c a l p r o g r e s s i o n s w i t h t h e same o u t e r v o i c e s as i n t h e u l t i m a t e r e d u c t i o n o f measures 9 and 10 which appears i n Example 3«19« g r e s s i o n d u r i n g measures 9 and 10 d i f f e r s i n two ways from t h o s e o f Example 3.20. The f i r s t i s t h a t t h e p r e s e n c e o f A as one o f t h e most i m p o r t a n t p i t c h e s i n measure 9» i n c o m b i n a t i o n w i t h E - f l a t , c r e a t e s some sense o f a dominant f u n c t i o n i n B - f l a t ; t h e p r o -g r e s s i o n s o f Example 3»20 have t h e s t a t i o n a r y t o n i c as one o f t h e i r most s i g n i f i c a n t f e a t u r e s . The v o c a l l i n e i n measure 9 a c t u a l l y s t a t e s t h e t r i t o n e o f V 7 o f B - f l a t , A - E - f l a t , and i t s r e s o l u t i o n t o B - f l a t and D, a g e s t u r e which foreshadows the appearance o f B - f l a t harmony i n measure 10 and emphasizes n t h e s u g g e s t i o n o f V' i n B - f l a t w h i c h comes w i t h t h e c h o r d i n Example 3.21. 86 The second d i f f e r e n c e between t h e harmonic p r o g r e s s i o n i n measures 9 and 10 and the p r o t o t y p e s o f Example 3 .20 stems from t h e premature a r r i v a l o f t h e n o t e D i n measure 1 0 ; i t i s brou g h t i n s i m u l t a n e o u s l y w i t h t h e d o u b l e - n e i g h b o r p a i r , F-s h a r p / G - f l a t - E, b e f o r e t h e p a i r r e s o l v e s t o F, r a t h e r t h a n o c c u r r i n g , a s one might e x p e c t , w i t h F on t h e t h i r d b e a t o f measure 1 0 . T h e r e f o r e , t h e harmonic s t r u c t u r e o c c u p y i n g • b e a t s 1 and 2 o f measure 10 c o n t a i n s n o t o n l y t h e c r u c i a l p i t c h e s o f TS(V 7/V) i n B - f l a t ( F - s h a r p , B - f l a t , and E ) , b u t a l s o t h o s e o f TS(V 7/V) i n D ( B - f l a t , t h e " e a r l y " D , and G-s h a r p ) . S i n c e B - f l a t , D , and G-sharp appeared i n measures 5 and 7 as TS( i n D , when t h e y r e t u r n i n measure 1 0 , im-m e d i a t e l y f o l l o w i n g T S ( V 7 ) i n D , we a r e aware o f t h e i r po-t e n t i a l t o assume t h e e a r l i e r f u n c t i o n once more, and t o r e -s o l v e t o the t o n i c o r dominant c h o r d o f D as shown i n Example 3 . 2 2 . Example 3 .22 t The h i n t o f T S ( V 7 / y ) i n D , b r o u g h t on by t h e p i t c h e s B - f l a t , D , and G-sharp i n measure 10. \ . D f T S ( V 7 ) T S ( V 7 A ) ~ - . - . - . - J a i _ - - _ _ y l / . 8 7 Measure 10 i s i m p o r t a n t i n e x p r e s s i n g the l i n k between B - f l a t and D key a r e a s which was emphasized a t the o u t s e t o f t h i s d i s c u s s i o n , and i s r e c a l l e d i n Example 3.23. Example 3«23: The e q u i v a l e n c e between lb 7 o f B - f l a t and TS(V7/V) o f D. A r e m i n d e r o f t h e f i r s t t o n i c o f the p i e c e , B, and i t s r e l a t i o n t o B - f l a t i s p r e s e n t i n measure 10, i n t h e form o f TS(V 7/V) o f B - f l a t , which c o u l d a l s o a c t as V 7 o f B. The passage from measure 7 t o 10 might even be s a i d t o h i n t a t a s h i f t from t h e dominant o f D t o t h a t o f B, as r e p r e s e n t e d i n Example 3'24, u n t i l the d o u b l e - n e i g h b o r r e s o l u t i o n o f F-sharp and E t o F t a k e s p l a c e a t t h e end o f measure 10, p r o v i n g B-Example 3.24: The h i n t o f V 7 o f B i n measure 10. ' / r ~ Op \i i\ 8 1 V 9 1 0 / DT 11- - TS ( -B: V 7 ? f l a t t o be t h e g o a l r a t h e r t h a n B. We may now add t o t h e s k e t c h begun i n Example 3*14 o f page 80, w h i c h t r a c e d t h e p r o g r e s s o f t h e harmonic v o i c e t h a t commenced on t h e t o n i c , B, and f e l l t h r o ugh B - f l a t t o A by measure 6. We see t h a t t h e d e s c e n t from B - f l a t t o A i s sim-88 p l y r e p e a t e d i n measures 7-8, b u t t h a t i t i s r e v e r s e d i n measures 9-10 (Example 3.25). Example 3»25« C o n t i n u a t i o n o f Example 3.14 from page 80; t h e p r o g r e s s o f the harmonic v o i c e from t h e i n i t i a l t o n i c , B, t h r o u g h B - f l a t and A, and now back t o B - f l a t . C r u c i a l t r i -t o n e s a t " ( X ) " . — Measures 10, 11, and the b e g i n n i n g o f 12 a r e complete-l y c o n c e r n e d w i t h t h e em b e l l i s h m e n t o f I ^ 7 i n B - f l a t by TS ( v 7 / v ), as Example 3*26 shows. A "whole-tone" v e r s i o n o f TS(V 7/V) o c c u r s , w h i c h i n c l u d e s D ( i n p l a c e o f t h e more con-v e n t i o n a l C - s h a r p / D - f l a t ) and G-sharp, i n a d d i t i o n t o the c r u -c i a l p i t c h e s , F - s h a r p / G - f l a t , B - f l a t , and E. T h i s r e s u l t s i n the s t a t i o n a r y t o n i c ( B - f l a t ) and i t s t h i r d (D) b e i n g h e l d t h r o u g h o u t measures ISO t o 12, and i n o u r h e a r i n g B - f l a t h a r -mony as p r o l o n g e d f o r t h e d u r a t i o n o f t h e pa s s a g e . The f u n c -t i o n s I ^ 7 and T S ( V 7 / v ) r e f e r o n l y t o t h e v e r y l o c a l r e l a t i o n -s h i p e x p r e s s e d i n th e s e measures, as t h e a r r i v a l a t measure 13 s u g g e s t s t h e f u n c t i o n V 7 o f E - f l a t f o r t h e B - f l a t major-m i n o r - s e v e n t h c h o r d , as i n measures 4 t o 8 (Example 3*26). As was done i n measures 4 and 7, G i s i n f e r r e d t o com-p l e t e t h e E - f l a t major c h o r d o f measure 13. S i n c e G i s de-p i c t e d as such a s t r u c t u r a l l y i m p o r t a n t p i t c h , i t s i n f e r e n c e i n Example 3*26 must be j u s t i f i e d . 89 Example 3.26: The prolongation of a B - f l a t major-minor-seventh chord i n measures 10 to 12, i t s embellishment by TS (V7/V) of B - f l a t , and i t s resolution as V7 of E - f l a t to I i n measure 13• J * 9 r r r r n • - •- — - - — — . - . - -^ — 1  >-• — - -E : V7-(At the points **, the B - f l a t major-minor-seventh chord i s embellished by TS(V7/V) of B - f l a t . ) 9 0 A most c o n v i n c i n g p o i n t can be made r e g a r d i n g t h e im-p l i c i t p r e s e n c e o f G i n t h e v o c a l l i n e , on t h e f i r s t b e a t o f measure 1 3 « The v o c a l p h r a s e b e g i n n i n g i n t h a t measure b e a r s a marked resemblance t o t h a t w i t h which the p i e c e began; Ex-ample 3 * 2 7 compares the two p h r a s e s . Example 3 * 2 7 * The v o c a l p h r a s e s o f measures 1 - 2 and 1 3 - 1 5 -Measures 1 - 2 : \f\) a. #* \r— - ^ T J - T - — .tJ i f " H r r measures 1 3 - 1 5 The i m p o r t a n t d i f f e r e n c e s between t h e s e two p h r a s e s a r e : ( i ) t h e t r a n s p o s i t i o n up a semitone o f t h e measure 1 3 p h r a s e ; ( i i ) t h e g r e a t e r l e n g t h o f t h e measure 1 3 p h r a s e , caus-ed by t h e i n s e r t i o n o f E - n a t u r a l between F and E-f l a t and t h e a d d i t i o n o f D t o t h e end o f t h e p h r a s e ; ( i i i ) t h e o m i s s i o n o f t h e f i r s t p i t c h o f t h e measure 1 3 p h r a s e , which would be G. t o c o r r e s p o n d t o t h e F-sh a r p o f measure 1 . The t h i r d i t e m o f d i f f e r e n c e argues f o r the i n f e r e n c e o f G tinder d i s c u s s i o n . I n a d d i t i o n t o t h i s , e x p e c t a t i o n o f G r e -s u l t s from t h e p r o l o n g a t i o n o f t h e B - f l a t m a j o r - m i n o r - s e v e n t h c h o r d from measures 1 0 t o 1 2 , and becomes i n t e n s i f i e d by c e r -t a i n e v e n t s a t t h e end o f measure 1 2 s the harmonic v o i c e be-g i n n i n g w i t h t h e E and F i n t h e v o c a l l i n e i s c o n t i n u e d by E-sharp and F-sharp i n t h e p i a n o t r e b l e , and t h e l a t t e r two 91 p i t c h e s a r e s t a t e d i n o c t a v e s , r e s u l t i n g i n a s t r o n g , c h r o -m a t i c r i s e t o ward G. T h i s makes t h e A o f measure 13 sound l i k e an a p p o g g i a t u r a t o G. A l l o f t h e s e f a c t o r s , combined w i t h t h e a c t u a l : p r e s e n c e o f G a t t h e b e g i n n i n g o f measure 7 i n the v o c a l l i n e (where the same c h o r d o c c u r s i n t h e accom-paniment as b e g i n s measure 13)1 a l l o w G t o be i n f e r r e d . There i s i r o n y i n t h e t h r e e d i f f e r e n c e s between the v o c a l p h r a s e s o f measures 1-2 and 13-15 mentioned on page 90. I t l i e s i n t h e f a c t t h a t t h e second and t h i r d f a c t o r s r e p r e -s e n t a d j u s t m e n t s t o t h e l a t e r p h r a s e which c o n t r a d i c t i t s t r a n s p o s i t i o n up a semitone and make i t more s i m i l a r t o t h e p h r a s e o f measures 1-2 i n terms o f p i t c h - c l a s s c o n t e n t . We r e c a l l t h a t t h e f i r s t v o c a l p h r a s e descended from F-sharp t o D i n two s t a g e s , F-sharp t o F, and E to D, and t h a t t h i s oc-c u r r e d as p a r t o f a p r o g r e s s i o n a l o n g t h e c y c l e o f f i f t h s i n B from V ^ / i i t o i . In measures I 3 - I 5 , the t r a n s p o s e d p h r a s e s t i l l descends from F-sharp t o D and t h e r e b y a l l o w s f o r a s i m i l a r harmonic p r o g r e s s i o n , due t o t h e m o d i f i c a t i o n s shown i n Example 3*28. T h i s example compares the v o c a l p h r a s e i n measures 13-15 w i t h a h y p o t h e t i c a l , e x a c t t r a n s p o s i t i o n o f t h e p h r a s e i n measures 1-2, as w e l l as w i t h t h e o r i g i n a l open-i n g p h r a s e . S i n c e t h e harmonic p r o g r e s s i o n accompanying the f i r s t v o c a l p h r a s e [ l i n e ( i i i ) o f Example 3.28, page 92] a r r i v e s on t h e t o n i c , B, t h e new p h r a s e i n measures 13-15 has the p o t e n -t i a l t o r e t u r n t o t h a t t o n i c w i t h a s i m i l a r p r o g r e s s i o n . Be-g i n n i n g w i t h t h e p r o g r e s s i o n i n measure 13 from an E - f l a t ma-j o r c h o r d t o TS(V?) o f E - f l a t , which s u p p o r t s t h e i n f e r r e d G 92 Example 3.28$ L i n e ( i ) shows t h e e x a c t t r a n s p o s i t i o n up a semitone o f t h e v o c a l p h r a s e from measures 1-2, l i n e ( i i ) t he a c t u a l p h rase o f measures 13-15i and l i n e ( i i i ) t h a t o f measures 1-2. N o t i c e t h a t t h e o m i s s i o n o f t h e i n i t i a l G and t h e a d d i t i o n s o f E and D which a r e made i n l i n e ( i i ) s e r v e t o make i t more s i m i l a r t o l i n e ( i i i ) . L i n e ( i i ) L i n e ( i i i ) 3£ 4 0 • 1 w 1 k — ^r—k i hi Y— w I and t h e a c t u a l F-sharp o f the v o c a l l i n e , one can e a s i l y i m a gine a c o n t i n u a t i o n t o V 7 / v o f B o c c u r r i n g where t h e v o i c e s t a t e s F/E-sharp. The c o n n e c t i o n between T S ( V 7 ) o f E - f l a t and V'/V °f B would be a s i m p l e one o f m i n o r - t h i r d - r e l a t e d s e v e n t h c h o r d s , as shown i n Example 3.29. Example 3.29s 13 h i <jtt 4 (15) E | ? , I - — T S ( V 7 ) •J-^^ZmL~u-_ 1. H y p o t h e t i c a l c o n t i n u a t i o n Bs r 7/V- ( i ) 93 The p r o g r e s s i o n i n Example 3.29 i s s u r p r i s i n g l y l i k e what a c t u a l l y happens. Measure 14 p r e s e n t s V 7 and a h i n t o f I^7 i n B, s u p p o r t i n g t h e E and E - f l a t / D - s h a r p o f the v o i c e , n as Example 3'30 i n d i c a t e s . However, V o f B i s n o t p r e p a r e d Example 3*30' Harmonic v o i c e summary o f measures 13-15» t o be compared w i t h Example 3 « 2 9 « daB ich mei - ne Wan et sous ses pieds im ge brei pla - ca te, ties XJ)P etteas drfingend 14 ML •e-15 i > f r ? t ft F7 4' y ^ 4 *1 . E ^ i I —-TS(V 7) (PII o f D, r e l a t i v e key t o B) B: V 7- ;|?7 TS(V 7/V) 94 by V 7/V as i n Example 3.29; i n s t e a d t h e same double appog-g i a t u r a ( t o t h e f i f t h and s e v e n t h ) o f V 7 o c c u r s as t h a t which e m b e l l i s h e d V 7 o f D i n measures 6 and 8 (Example 3.31). Example 3«3l« Double a p p o g g i a t u r a f i g u r e s from meas-u r e s 6 and 8, and measure 14. m.6,8s V 7 o f D m . l 4 i V 7 o f B I t i s i m p o r t a n t t o n o t e t h a t , by n o t p r e p a r i n g V 7 o f B w i t h V 7/V, Schoenberg p r o l o n g s t h e l e a d i n g - t o n e , B - f l a t / A -s h a r p , f o r l o n g e r , a v o i d i n g r e s o l v i n g i t u n t i l t h e t o n i c harmony a r r i v e s a t t h e end o f measure 14. ( I n Example 3.29, which does use t h e V 7/V t o approach V 7 , B - f l a t moves t o B a t th e b e g i n n i n g o f measure 14, and back t o A-sharp f o r V 7 b e f o r e t h e more i m p o r t a n t r i s e t o B a t the end o f the measure.) With t h e t h i r d b e a t o f measure 14, t h e two c r u c i a l harmonic v o i c e m o t i o n s o f a V 7 - I cadence i n B o c c u r (E t o E^ f l a t / D - s h a r p , and B - f l a t / A - s h a r p t o B ) . The f o r m e r m o t i o n i s s t a t e d i n v o i c e and p i a n o , and t h e l a t t e r appears i n the h i g h e s t v o i c e o f t h e accompaniment, r e n d e r i n g b o t h c o n s p i c u o u s d e s p i t e t h e c o n f l i c t i n g p r e s e n c e o f C-sharp and G i n t h e t o n i c c h o r d , h e l d o v e r from V 7 ^ 9 ) # The b r i e f t o n i c harmony passes i m m e d i a t e l y t o TS(V 7/V) a t t h e b e g i n n i n g o f measure 15, a p r o g r e s s i o n which r e s e m b l e s t h a t from the end o f measure 2 i n t o measure 3. The main d i f f e r e n c e between t h e two i s t h a t t h e t o n i c harmony o f measure 2 ended t h e f i r s t v o c a l p h r a s e and t h e TS( V 7/V) o f measure 3 "began t h e n e x t , w h i l e , i n meas-95 u r e s lk and 15, t h e extended v o c a l p h r a s e encompasses b o t h the t o n i c and TS(V 7/V) f u n c t i o n s . A c o m p a r i s i o n o f measures 1-3 and 13-15 i s made i n Example 3.32. Example 3*32: Measures 1-3 and 13-15 compared; stemmed h a l f - n o t e s a r e t h o s e found i n t h e main d e s c e n t o f t h e v o c a l l i n e i n each passage. Common t o b o t h passages i s t h e p r o g r e s -s i o n : V 7 - - - I - — T S ( V ? / V ) i n B. measures 1-3 measures 13-15 (v 7/v) The a r r i v a l a t TS(V 7/V) i n measure 15 marks the r e t u r n o f B - f l a t / A - s h a r p t o B, and what f o l l o w s i s e s s e n t i a l l y a coda. Example 3*25 o f page 88, which d e p i c t e d the l o n g - r a n g e p r o g r e s s o f t h e harmonic v o i c e b e g i n n i n g w i t h t h e t o n i c B o f measure 2, may now be d o n t i n u e d as i n Example 3«33« The hy-p o t h e t i c a l , b r a c k e t e d p o r t i o n o f Example 3-33 i s i n c l u d e d t o c l a r i f y t h e e f f e c t which t h e TS(V /V) c h o r d o f measure 15 p o t e n t i a l l y h a s ; approached by t h e dominant-seventh c h o r d o f B, i t s u b s t i t u t e s f o r t h e t o n i c , e n a b l i n g m o t i o n from t h e l e a d i n g - t o n e t o t h e t o n i c t o o c c u r w h i l e the s u p p o r t i n g h a r -monic p r o g r e s s i o n a c t u a l l y r e g r e s s e s from t h e dominant t o t h e f u n c t i o n w h i c h i m m e d i a t e l y p r e c e d e s i t a l o n g the c y c l e o f 96 f i f t h s i n B. T h i s makes us a n t i c i p a t e a n o t h e r approach o f Example 3'33* C o n t i n u a t i o n o f Example 3.25, page 88; t h e r e t u r n t o the t o n i c , B, o f t h e harmonic v o i c e which began t h e r e i n measure 2. The i m p o r t a n t t r i t o n e s a r e a t t h e p o i n t s ( X ) . (X) (X) 4 1 r — , (X) ( X ) ( s-fa-^ 0 *y ^V^f >f'f ff>f I m. 2 3 4-5 6 7 8 9 10 14 15 expected? t h e t o n i c which w i l l p r o v e t o be a c o n c l u s i v e V^-I cadence, as shown i n t h e b r a c k e t s . C e r t a i n p i t c h e s in* t h e l a s t f o u r measures o f t h e p i e c e c o n s t i t u t e a r a t h e r o b s c u r e v e r s i o n o f the e x p e c t e d attempt t o a c h i e v e a cadence on t h e B t o n i c . The i n i t i a l s t e p toward t h i s r e s o l u t i o n i s t h e convergence o f the t r i t o n e o f T S ( V 7 / V ) , B - F/E-sharp, back t o F-sharp - A-sharp o f V 7. T h i s essen-t i a l l y o c c u r s i n t h e c o u r s e o f measures 16 and 17, a l t h o u g h p i t c h e s which c o n t r a d i c t t h e sense o f V o f B which would r e -s u l t from t h e bare r e s o l u t i o n seen as Example 3*34, Example 3.34: a r e a l s o p r e s e n t . E x t r a c t i n g o n l y t h o s e p i t c h e s which p a r t i -c i p a t e i n harmonic f u n c t i o n s w h ich, i n i s o l a t i o n , a re i n t e r -9 7 p r e t a b l e w i t h r e s p e c t t o B y i e l d s a p r o g r e s s i o n from TS(V 7/V) t h r o u g h V t o I (Example 3.35). Example 3'35s Measures 15 t o 18; the s u g g e s t i o n o f a cadence t o t h e B t o n i c . 98 O b v i o u s l y , so much e l s e o c c u r s i n measures 15 t o 18 which does n o t s u p p o r t a c a d e n t i a l f e e l i n g i n B t h a t one h e a r s o n l y a h i n t o f t h e p r o g r e s s i o n shown i n Example 3»35» however, t h i s h i n t i s worthy o f d i s c u s s i o n because o f the abundance o f harmonic v o i c e m o t i o n t h r o u g h o u t t h e p i e c e which p o i n t s t o B as a t o n i c and t o D as a r e l a t e d key. (One h e s i t a t e s t o s p e c i f y t h e modes o f t h e s e k e y s , b u t the f a c t t h a t B o c c u r s f i r s t , i n measure 2, where i t s minor mode i s s u g g e s t e d , argues f o r t h e c o n v e n t i o n a l m i n o r / r e l a t i v e - m a j o r i n t e r p r e t a t i o n o f B and D.) Whether c o n s i d e r e d i n c o n t e x t o f a cadence t o B o r n o t , t h e emphasis upon B - f l a t / A - s h a r p i n t h e l a s t t h r e e measures o f t h e p i e c e i s u n d e n i a b l e , as i s t h e u l t i m a t e r e -s o l u t i o n o f t h a t p i t c h t o B. A l s o u n d e n i a b l e i s the impor-t a n c e o f t h e major t h i r d , B - f l a t - G - f l a t , which i s g r a d u a l l y a c h i e v e d by t h e f a l l o f B t o B - f l a t i n measure 15 and t h e r i s e o f F t o G - f l a t i n t h e f o l l o w i n g measure. As a f i n a l argument f o r t h e p r e s e n c e o f an o b s c u r e d V - I cadence i n B a t th e end o f t h e p i e c e , a p a r a l l e l may be drawn between t h e f i n a l two chords and t h o s e upon b e a t s 2 and 3 of measure 14. I n measure 14, we h e a r d a p r o g r e s s i o n from V' o f B th r o u g h a b r i e f I ^ 7 , w i t h t h e l a t t e r f u n c t i o n r e p r e s e n t e d by the p i t c h e s B, E - f l a t / D - s h a r p , and A. The f i n a l " t o n i c " c h o r d i n measure 18 a l s o c o n t a i n s t h e s e t h r e e p i t c h e s . N a t u r a l l y , t h e p r e s e n c e o f A i n t h e f i n a l c h o r d d e s t a b i l i z e s any t o n i c i m p l i c a t i o n s i n B, but i t does draw a t t e n t i o n t o th e s i m i l a r i t y between t h e f i n a l cadence and t h e much c l e a r e r p r o g r e s s i o n from V 7 t o I ^ 7 i n measure 14. Measure 14 and the 99 f i n a l cadence are compared i n Example 3«36. Example 3.36: Measure 14, b e a t s 2 and 3, and measures l ^ to 16; t h e s u g g e s t i o n o f V-I p r o g r e s s i o n s i n B. (Stemmed p i t c h e s a r e t h o s e f o u n d i n t h e v o c a l l i n e . ) One might a l s o h e a r a r e f e r e n c e to t h e p r o g r e s s i o n from V 7 i n measure 14 t o TS(V 7/V) i n measure 15 i n t h e f i n a l cadence. I n b o t h p r o g r e s s i o n s , t h e l e a d i n g - t o n e r e s o l v e s t o the t o n i c , b u t one has t h e sense o f a " d e c e p t i v e " cadence due t o t h e emphasis upon G i n the harmony which s u p p o r t s t h e t o n i c p i t c h . I n t h e f i n a l cadence, though, th e absence o f F i n the second .chord s u g g e s t s an o r d i n a r y V-VI p r o g r e s s i o n , r a t h e r t h a n V-T S ( V 7 / V ) , as shown i n Example 3.37. Example 3.37: The " d e c e p t i v e " cadence e f f e c t i n meas-u r e s 14-15 and 17-18. The m a t e r i a l i n measures 15 t o 18 which i s l e f t un-a c c o u n t e d f o r i n t h e p r e c e d i n g "B" i n t e r p r e t a t i o n i s d i r e c t e d 100 toward two o t h e r t o n a l c e n t r e s , B - f l a t and G (members o f t h e o r i g i n a l complex, G - B - f l a t - B - D , i n t r o d u c e d a t t h e o u t s e t o f t h i s d i s c u s s i o n ) . We w i l l d e a l f i r s t w i t h t h o s e harmonic v o i c e m o t i o n s r e l e v a n t t o a " B - f l a t " i n t e r p r e t a t i o n o f the l a s t f o u r measures o f the p i e c e . To c o n s i d e r B - f l a t - r e l a t e d harmonic v o i c e s , we must f i r s t r e t u r n t o t h e p a r a l l e l drawn i n Example 3-32 between measures 1 t o 3 and 13 t o 15. That example ended w i t h c o r -r e s p o n d i n g TS(V 7/v) c h o r d s , b u t c o u l d have extended t o i n c l u d e one f u r t h e r c h o r d i n t o measures 3 and 15 (Example 3 '38) . Example 3.38: \7- y 1 I n measure 3t t h e above c h o r d was i n t e r p r e t e d as V o f J?II i n D, on the s t r e n g t h o f t h e e v e n t s which f o l l o w e d i n measure 4: h e r e , i n measure 15» i t i s s t i l l h e a r d p r i m a r i l y as a B - f l a t c h o r d , but i n s t e a d o f i t s b e i n g f o l l o w e d by J 5 l l 7 and V o f D, elements o f i t s own dominant are i n t r o d u c e d . T h i s i s most o b v i o u s i n t h e v o c a l p a r t , which i s e s s e n t i a l l y c o n c e r n e d w i t h t h e p i t c h e s F, E - f l a t , and A t h r o u g h o u t meas-u r e s 16 t o 18 (Example 3 .39). Example 3'39* The v o c a l l i n e i n measures 16 t o 18 . 101 On t h e second b e a t s o f measures 16 and 17» where E-f l a t o c c u r s i n t h e v o c a l l i n e , t he p i a n o accompaniment sup-p l i e s A, f o r m i n g t h e t r i t o n e o f V 7 o f B - f l a t . I n a l t e r n a t i o n w i t h t h e s e s t a t e m e n t s o f E - f l a t - A a r e chords c o n t a i n i n g the p i t c h e s C and B - f l a t , t o which t h e t r i t o n e would r e s o l v e i n a V'-I cadence i n B - f l a t . I n Example 3'40, t h e harmonic v o i c e s which p a r t i c i p a t e i n t o n i c and dominant f u n c t i o n s i n B - f l a t from measures 15 t o 18 a r e presented} t h e example s h o u l d be compared w i t h Example 3«35t which d i d t h e same f o r f u n c t i o n s i n B. Example 3*40: Measures 15-18, w i t h emphasis upon the B - f l a t - r e l a t e d harmonic v o i c e s . mel un ten - drai~ ter Ih - rer Soh mon hum - ble jou W i nit n * : „ *» _ ' 4* ' ^ - - t jr-= -> fr* * G rVs— ^ -b-^ 1 V [ t> fi— ^ ~ l i fe^-B K vi£~ I V 7 T S ( V 7 ) 102 Example 3.40 p r o v e s t o be e a s i e r t o h e a r t h a n Example 3.25 when t h e two a r e compared. T h i s i s because the main harmonic v o i c e o f 3.40, which i n v o l v e s B - f l a t and A, i s a c t u -a l l y t r e a t e d as a v o i c e i n t h e m u s i c , and appears as t h e h i g h -e s t p a r t i n t h e accompaniment, whereas t h e c o r r e s p o n d i n g l y i m p o r t a n t harmonic v o i c e o f 3.25, i n v o l v i n g A-sharp and B, i s o b s c u r e d . S e v e r a l o c t a v e t r a n s f e r s are r e q u i r e d t o d e r i v e th e l a t t e r , and f u r t h e r m o r e , B - f l a t / A - s h a r p and B a r e h e a r d s i m u l t a n e o u s l y on t h e t i e d - o v e r t h i r d b e a t s o f measures I5 i 16, and l?t t h w a r t i n g t h e sense o f harmonic v o i c e m o t i o n from one p i t c h t o t h e o t h e r which Example 3*25 s u g g e s t s o c c u r s o v e r th e b a r - l i n e s . The v a l i d i t y o f Example 3'25 would depend h e a v i l y upon the p r e c e d e n t s e t from t h e b e g i n n i n g o f the p i e c e t h a t B i s r e l e v a n t as a t o n i c c e n t e r , w h i l e Example 3'40 i s s e l f - e x p l a n -a t o r y d e s p i t e t h e l a c k o f p r e c e d e n t o f B - f l a t as a t o n i c . However, a d d i t i o n a l remarks a r e n e c e s s a r y f o r a f u l l u n d e r s t a n d i n g o f Example 3*40. I t w i l l have been n o t e d , no d o u b t , t h a t t h e motions from B - f l a t t o A i n measures 15-16 and 16-17 a r e shown t o be s u p p o r t e d by p r o g r e s s i o n s from I t o V 7 i n B - f l a t , whereas the f i n a l cadence i s i n t e r p r e t e d as I t o T S ( V 7 ) . The d i s t i n c t i o n between V 7 and T S ( V 7 ) i s exag-g e r a t e d i n Example 3'40; a l t h o u g h t h e f i n a l cadence does d i s -p l a y t h e o n l y o v e r t m o t i o n from B - f l a t t o B, t h e l a t t e r p i t c h i s s t i l l p r e s e n t each o f t h e two p r e c e d i n g t i m e s t h a t B - f l a t descends t o A f o r V 7 o f B - f l a t . T h i s means t h a t t h e V 7 chords a c t u a l l y have l o w e r e d f i f t h s , making them d i s t i n g u i s h a b l e from T S ( V 7 ) o n l y i f one judges F t o be o f g r e a t e r i m p o r t a n c e t h a n B. 103 Such a judgement i s made i n Example 3'40 because the v o c a l l i n e emphasizes F, and n o t B, and because V 7 i s t h e more immediate o f t h e two f u n c t i o n s . The t h i r d t o n a l c e n t e r which was s a i d t o be i m p l i e d i n measures 15 t o 18 i s G. The case f o r t h i s t o n i c r e s t s upon t h r e e s t a t e m e n t s o f t h e p e r f e c t f i f t h , D t o G, t h e l a s t o f which i s accompanied by d i r e c t harmonic v o i c e m o t i o n from F-sharp t o G. The fundamental weakness i n t h i s case stems from t h e f a m i l i a r i t y which we have d e v e l o p e d w i t h the c h o r d , i n t h e r o l e o f TS(V 7/V) i n B, based upon o c c u r r e n c e s o f t h a t f u n c t i o n i n measures 3 and 15' I f we a r e a b l e t o l i s t e n t o t h e l a s t f o u r measures o f music i n c o n t e x t o f a proposed G t o n i c , t h e n t h e p i t c h e s o f t h e above c h o r d which appear a t the b e g i n n i n g o f measures 16, 17, and 18 (G, B, and F) may be s a i d t o r e p r e s e n t I ^ 7 i n G: t h e f i n a l c h o r d o f t h e p i e c e c o u l d be i n t e r p r e t e d as the complete I c h o r d . I n a l t e r n a t i o n w i t h t h e I ^ 7 chords would be dominant c h o r d s i m p l i e d by t h e p i t c h e s D and F-sharp. Example 3.42 d e p i c t s t h e f u n c t i o n a l harmony i n G which can be i n f e r r e d from measures 15 t o 18. H a v i n g c o n s i d e r e d t h r e e i n t e r p r e t a t i o n s o f measures 15 t o 18, each b i a s e d i n s u p p o r t o f a d i f f e r e n t t o n a l c e n t e r , i t i s n e c e s s a r y t o c o n s i d e r t h e i r i n t e r r e l a t i o n and t o determine what g e n e r a l p r i n c i p l e s make such d i v e r s i t y p o s s i b l e i n a s i n -g l e passage. The examples t o be r e f e r r e d t o i n t h i s r e g a r d a r e 305i 3«40, and 3.41, which d e a l t w i t h B, B - f l a t , and G, 104 r e s p e c t i v e l y (see pages 971 101, and 104 f o r t h e s e examples). Example 3.41: F u n c t i o n a l harmony i n r e l a t i o n t o G i n measures 15-18. 1(?7 v#5 1^ 7 -v#5 l v The s i m p l e s t way o f o b s e r v i n g how examples 3'35» 3'40 and 3'41 i n t e r r e l a t e i s t o p l a c e t h e f u r t h e s t r e d u c t i o n s i n each example i n a column and "sum" them up on a f o u r t h s t a f f t o show t h e f u l l complexes o f p i t c h e s from which t h e y have been drawn. T h i s s h o u l d r e s u l t i n something c l o s e t o t h e a c t u a l s c o r e , b u t condensed i n t o harmonic v o i c e n o t a t i o n (see Example 3.42, page 105). Example 3'42 p r e s e n t s two b a s i c s t r u c t u r e s : an aug-mented t r i a d , and a f i v e - p i t c h , "whole-tone" c h o r d . The l a t -t e r c o n t a i n s t h e r o o t s , t h i r d s , and se v e n t h s o f t h r e e d i f f e r -ent m a j o r - m i n o r - s e v e n t h c h o r d s , making e i t h e r t h e m i n o r - s e v -e n t h o r d o u b l e - n e i g h b o r f u n c t i o n o f any one o f them a p o s s i b l e 105 Example 3.42: The amalgamation o f Examples 3 . 3 5 , 3.40, and 3.41. on t h e f o u r t h s t a f f , t h e i m p o r t a n t augmented t r i a d i s l a b e l l e d "A", and t h e "whole-tone" c h o r d "WT". From 3-35« B~s i — T S ( v 7 7 v •) - m r — ~ v#5- - - - TS"( v 7 / v " ) — v # 5 - — i - ^ From 3.40 : I v ' I# 5 — T S ( V 7 ) From 3.41: * { i f f f 1 } ^ ? G: v#5- • l)?7 v # 5 — i ' " T o t a l 1 i r 1 " " i n f f p A M«P A T«rm t * -___WT_ A- ,---,-WT -A WT (no F) i n t e r p r e t a t i o n o f t h e e n t i r e s t r u c t u r e (Example 3«43)« The augmented t r i a d i s i n t e r p r e t e d as a d i f f e r e n t major t r i a d w i t h r a i s e d f i f t h i n each o f i t s i n v e r s i o n s ; on an F-sharp r o o t , i t i s V#5 i n B (3*35); on B - f l a t , I#5 i n B - f l a t ( 3-40); and on D, V#5 i n G ( 3.41). To c l o s e t h i s d i s c u s s i o n o f Opus 15i Number 5 i a s k e t c h o f t h e e n t i r e p i e c e , i n two l e v e l s , i s p r e s e n t e d i n Example 3 . 4 4 on page 107. The f i r s t l e v e l i s s i m p l y a u n i o n o f t h e examples p r e s e n t e d h i t h e r t o ; t h e second r e c o g n i z e s a r e a s o f p r o l o n g a t i o n s u g g e s t e d by t h e absence o f mo t i o n i n 106 Example 3«43s The "whole-tone" c h o r d o f measures 16-18, and t h e p r e s e n c e t h e r e i n o f t h e r o o t s , t h i r d s , and sev-enths o f m a j o r - m i n o r - s e v e n t h chords on B, F, and G. t h e uppermost harmonic v o i c e , which b e g i n s on the f i r s t t o n i c o f the p i e c e , B. The p r o g r e s s o f t h i s v o i c e was t r a c e d i n examples 3.14 (page 80), 3.25 (page 88), and 3 0 3 (page 96); i t s placement above the o t h e r s i n l e v e l two o f Example 3*44 i s t o emphasize i t s r o l e i n d e f i n i n g t h e s t r u c t u r e o f t h e p i e c e . The upper v o i c e i s a c t e d upon by o t h e r v o i c e s , which f o r c e i t t o move up o r down by f o r m i n g t r i t o n e s w i t h i t . The f a c t t h a t i t moves l e s s o f t e n t h a n t h e l o w e r v o i c e s s u g g e s t s t h a t i t w a i t s u n t i l t he s t r e s s o f d i s s o n a n c e p l a c e d upon i t i s so i n t o l e r a b l e as t o demand m o t i o n . F o r example, the s t r e s s upon t h e i n i t i a l B r e s u l t s from E-sharp/F i n measure 3» and B descends t o B - f l a t t o r e -l i e v e i t ; s k i p p i n g t o measure 9» t h e p i t c h A o f t h e upper 107 Example 3«^s Harmonic v o i c e summary o f Opus 15» Number 5» 108 v o i c e i s p r e s s u r e d by t h e i n t r o d u c t i o n o f E - f l a t , and r e a c t s by r i s i n g .back t o B - f l a t ; i n t u r n , t h e p i t c h E i n measure 14 f o r c e s B - f l a t / A - s h a r p up t o B once more. The o n l y m o t i o n o f the upper harmonic v o i c e which i s n o t d i c t a t e d by the d i r e c t f o r m a t i o n o f a t r i t o n e w i t h one o f i t s members i s the descent from B - f l a t t o A which o c c u r s o v e r measures 4 to 6 and i s r e -p e a t e d i n 7 to 8; i n t e r e s t i n g l y , t h i s m o t i o n i s a l s o the o n l y one which m i g h t be c o n s i d e r e d p a r t i a l l y u n s u c c e s s f u l , s i n c e B - f l a t does r e m a i n as the m i n o r - n i n t h o f V 7 o f D, w i t h t h e A which may be s a i d to r e p l a c e i t on a more fundamental l e v e l . One m i g h t be tempted t o show B - f l a t as p r o l o n g e d t h r o u g h measures 4 t o 14, making t h e m o t i o n i n the upper v o i c e a s i m p l e l o w e r - n e i g h b o r f i g u r e , B - B - f l a t / A - s h a r p - B. The s u p p o r t i n g harmonic p r o g r e s s i o n f o r t h i s f i g u r e which o c c u r s i n Opus 15» Number 5 i s shown on t h e f i r s t s t a f f o f Example 3»45» The second s t a f f shows a c o n v e n t i o n a l p r o g r e s s i o n w hich might be e x p e c t e d t o accompany such an upper v o i c e i n a more t r a d i t i o n a l l y t o n a l p i e c e . Example 3.45: measure: 2 3 5 , 7 6,8 10-12 14 15 109 CHAPTER IV AN ANALYSIS OF OPUS 15, NUMBER 11 The o p e n i n g measure o f Opus 15» Number 11 p r e s e n t s a B - f l a t m i n o r t r i a d , s t a t e d e x p l i c i t l y i n t h e p i a n o t r e b l e and s u p p o r t e d s u b t l y i n t h e b a s s . The p r o g r e s s o f t h i s c h o r d t o the C - s h a r p / D - f l a t m a j o r - m i n o r - s e v e n t h c h o r d o f measure 5 depends on a s i n g l e harmonic v o i c e m o t i o n — t h a t from B - f l a t t o B - n a t u r a l . T h i s m o t i o n a c t u a l l y o c c u r s i n measure 1, w i t h t h e f i n a l p i t c h o f the s i x t e e n t h - n o t e r u n i n t h e bass c l e f , a C - f l a t j however, t h e t r u e a r r i v a l o f t h e C - s h a r p / D - f l a t c h o r d i s d e l a y e d by t h e mo t i o n from D - f l a t t o D - n a t u r a l which o c c u r s a t t h e end o f measure 1. Example 4.0 shows b o t h o f t h e s e harmonic v o i c e m o t i o n s . (So t h a t i n d i v i d u a l examples may be seen i n c o n t e x t o f t h e e n t i r e p i e c e , a r e p r o d u c t i o n o f Opus 15, Number 11 i s p r o v i d e d on pages 111 and 112, i n Example 4.1.) The r e a d e r w i l l have n o t i c e d t h a t t h e p i t c h e s o f t h e B - f l a t minor t r i a d which a r e e x t r a c t e d from t h e s i x t e e n t h -n o t e r u n and i n c l u d e d i n l e v e l s 1 and 2 o f Example 4.0 (page 110) a r e n o t u n i f o r m l y emphasized e i t h e r by t h e manner i n which t h e r u n i s beamed o r by t h e way i n which i t a l i g n s w i t h t h e b e a t s o f measure 1. However, an a u r a l c o n n e c t i o n i s c e r t a i n l y made between t h e p i t c h e s i n t h e r i g h t - h a n d p o r t i o n o f t h e p i a n o accompaniment and t h e i r r e p e t i t i o n s i n d i f f e r e n t 110 o c t a v e s i n the l e f t . The f o l l o w i n g p o i n t s s u g g e s t why we make such a c o n n e c t i o n , beyond the b a s i c r e a s o n t h a t we p e r c e i v e o c t a v e - r e l a t e d p i t c h e s as b e i n g s i m i l a r . (1) A B - f l a t minor t r i a d i s t h e f i r s t complete, t h r e e -I l l 112 Example 4.1, c o n t i n u e d . 113 v o i c e d harmony we h e a r . The f i r s t i n t e r v a l i n t h e s i x t e e n t h -n o t e r u n which a l l o w s us t o d i s c e r n t h e pr e s e n c e o f more than one harmonic v o i c e i n t h e p i a n o bass i s the f i r s t t h a t i s g r e a t e r t h a n a w h o l e - t o n e — t h e major t h i r d , F t o D - f l a t . I t s two p i t c h e s must be i n t e r p r e t e d as b e l o n g i n g t o d i f f e r e n t h a r -monic v o i c e s by t h e d e f i n i t i o n o f harmonic v o i c e p r e s e n t e d i n Ch a p t e r I . With t h e B - f l a t o f t h e p i a n o t r e b l e , F and D - f l a t form the f i r s t s t r u c t u r e i n t h r e e harmonic v o i c e s : a B - f l a t m i n o r t r i a d . Because o f f u r t h e r s t a t e m e n t s o f t h e s e t h r e e p i t c h - c l a s s e s , we h e a r them as p r o l o n g e d u n t i l new members o f t h e i r r e s p e c t i v e harmonic v o i c e s c o n t r a d i c t them, as do t h e C - f l a t / B - n a t u r a l and D - n a t u r a l which o c c u r l a t e r i n t h e meas-ur e . (2) P i t c h - c l a s s r e p e t i t i o n s i n the s i x t e e n t h - n o t e r u n  emphasize t h e B - f l a t m i n o r t r i a d . The p o i n t a t which t h e s i x t e e n t h - n o t e r u n f i r s t r e p e a t s a p i t c h - c l a s s i s i n t h e second q u a r t e r o f b e a t 2, where G - f l a t moves t o F, as i t d i d an o c t a v e h i g h e r a t the b e g i n n i n g o f t h e r u n . The two p i t c h e s were i n t e r p r e t e d as an upper n e i g h b o r and i t s r e s o l u t i o n t o th e f i f t h o f t h e B - f l a t m i n o r t r i a d when t h e y f i r s t o c c u r r e d ; th e same i n t e r p r e t a t i o n i s v a l i d f o r t h e i r second appearance, an o c t a v e l o w e r , as i t c o i n c i d e s w i t h D - f l a t o f t h e p i a n o t r e b l e and t h e memory o f B - f l a t i s s t i l l f r e s h . The o n l y o t h e r p i t c h - c l a s s which i s s t a t e d more th a n once i n t h e s i x -t e e n t h - n o t e r u n i s C - f l a t / B - n a t u r a l , b u t t h e f i r s t o f i t s two s t a t e m e n t s i s e f f e c t i v e l y c a n c e l l e d o u t by the more i m p o r t a n t B - f l a t t o which i t l e a d s , t h e l a t t e r p i t c h b e i n g the second B - f l a t which i s h e a r d as w e l l as t h e r o o t o f t h e p r e v a i l i n g 114 harmony. Even i f we i n c l u d e t h e p i t c h e s o f t h e p i a n o t r e b l e i n o u r s e a r c h , we f i n d no p i t c h - c l a s s r e p e t i t i o n save t h a t o f members o f the B - f l a t m i n or t r i a d (and t h e upper n e i g h b o r t o i t s f i f t h , G - f l a t / F - s h a r p , mentioned above). Example 4.2 i s e s s e n t i a l l y t h e same as l e v e l 3 o f Example 4.0s t h e s i n g l e a d d i t i o n o f G - f l a t as an upper n e i g h b o r t o F has been made. The importance o f G - f l a t i s th u s s u g g e s t e d a t an e a r l y s t a g e i n t h e p i e c e ; i t w i l l p r o v e t o be t h e t o n a l c e n t e r o f t h e e n t i r e work i n t h e c o u r s e o f t h i s a n a l y s i s . o f measure 2 , i s s u e s from what p r e c e d e s i t i n two ways. F i r s t , i t c o n t i n u e s t o b u i l d t h e d i m i n i s h e d c h o r d which t h u s f a r c o n s i s t s o f B, D, and F (Example 4 .4 ) . The p r e s e n c e o f G-s h a r p w i t h B and F i n measure 2, a l o n g w i t h t h e s t i l l - f r e s h sound o f D - n a t u r a l from measure 1, causes t h e new p i t c h , E-n a t u r a l t o sound l i k e an upper n e i g h b o r which may y e t r e -s o l v e back t o D, as shown i n Example 4.4. The second element o f d e r i v a t i o n o f t h e c h o r d o f measure 2 i n v o l v e s t o n a l harmonic v o i c e m o t i o n o f a d i f f e r e n t Example 4.2s The c h o r d (Example_A.3)_, Example 4.3$ 115 Example 4.4: — ^ ^ new v o i c e e n t e r s E as an upper n e i g h b o r t o D 3$ s o r t t h a n t h a t shown i n Example 4.4. The major t h i r d , E - G-s h a r p , i s t h e f i n a l member o f a c h a i n o f t h i r d s which has moved by d e s c e n d i n g p e r f e c t f i f t h s as shown i n Example 4.5.^ Example 4.5* L e v e l 1 L e v e l 2 L e v e l 3 PP 116 The harmonic o v e r s t a t e m e n t o f t h e c h a i n o f t h i r d s which i s shown i n l e v e l s 2 and 3 o f Example 4.5 i s v a g u e l y a u d i b l e when one l i s t e n s t o measures 1 and 2 o f the p i e c e . However, a t t h e p o i n t "**", Example 4.5 d i s t o r t s what i s a c t u a l l y h e a r d i n an e f f o r t t o p r o j e c t t h e c h a i n o f t h i r d s as r e p r e -s e n t a t i v e o f complete t r i a d s moving i n t r a d i t i o n a l f a s h i o n a l o n g th e c y c l e o f f i f t h s . The G - f l a t i n c l u d e d a t the p o i n t i s n o t a c t u a l l y h e a r d , and t h w a r t i n g any sense o f a C - f l a t major t r i a d which th e major t h i r d , C - f l a t - E - f l a t , might i t s e l f c r e a t e i s the p r e s e n c e o f F - n a t u r a l i n t h e r i g h t hand o f t h e p i a n o accompaniment, f o l l o w e d by D - n a t u r a l . The F- and D - n a t u r a l s s e r v e t o c a n c e l out G - f l a t and C - f l a t , r e s p e c t i v e l y , b e i n g newer members o f t h e same harmonic v o i c e s as G - f l a t and C - f l a t . However, i t would be i n c o n s i s t e n t n o t t o acknowledge the f u n c t i o n o f E - f l a t as a l e a d i n g - t o n e t o t h e E - n a t u r a l o f measure 2, i n a d d i t i o n to i t s more immediate s u b m i s s i o n to D - n a t u r a l a t t h e end o f measure 1, s i n c e s i m i l a r f u n c t i o n s were a t t r i b u t e d t o t h e c o r r e s p o n d i n g p i t c h e s , F and B - f l a t , o f t h e p r e c e d i n g major t h i r d s ( t h e y were shown to r i s e t o G - f l a t and C - f l a t / B - n a t u r a l , r e s p e c t i v e l y , i n Example 4.5)' Of c o u r s e , the two i n f e r r e d d e r i v a t i o n s f o r t h e measure 2 c h o r d must be r e c o n c i l e d ; i n o r d e r t o do t h i s , we must l o o k ahead t o measure 5» as t h a t i s where the f u n c t i o n o f t h e measure 2 c h o r d becomes c l e a r . The p r o g r e s s i o n i n measures 3 t o 5 o v e r t l y s u g g e s t s t h e f u n c t i o n s TS(V 7 / v ) and V 7 i n F -sharp. The former f u n c t i o n , which i s s u g g e s t e d by t h e d o u b l e - n e i g h b o r p a i r D - C, l a c k s F-117 s h a r p and, i n s t e a d , c o n t a i n s C-sharp and F/E-sharp, p i t c h e s which a n t i c i p a t e t h e dominant-seventh f u n c t i o n which i s t o come; Example 4.6 shows b o t h o f t h e s e f u n c t i o n s . Example 4.6: The f u n c t i o n s TS(V 7/V) and V 7 i n F-sharp i n measures 3-5 • 1 1 8 L e v e l 1 o f Example 4.6 shows t h e i n d i v i d u a l p a t h o f e v e r y harmonic v o i c e i n measures 2 t o 5» b e g i n n i n g from the d i m i n i s h e d t r i a d , B - D - F, a c h i e v e d by t h e end o f measure 1. The s i m p l e f a c t s about measure 2 are t h a t B and F con-t i n u e from measure 1 and t h a t a new harmonic v o i c e b e g i n s on G-sharp. C o m p l i c a t i o n s stem from t h e double f u n c t i o n o f E-n a t u r a l as ( i ) an upper n e i g h b o r t o t h e D - n a t u r a l which would 0 7 complete a v i i ' o f F-sharp, and ( i i ) as a p a s s i n g tone t o E-s h a r p o f t h e s o o n - t o - b e - a c h i e v e d dominant-seventh o f F-sharp. T h i s m u l t i p l i c i t y o f purpose i s r e p r e s e n t e d on l e v e l 1 by t h e i n c l u s i o n o f a D - n a t u r a l t i e d o v e r from measure 1 and shown t o sound i m p l i c i t l y w i t h t h e E - n a t u r a l . T h i s D - n a t u r a l c a r r i e s o v e r t o t h a t o f measure 3 which f u n c t i o n s i n t h e d o u b l e - n e i g h -b o r p a i r , D- C/B-sharp, which p r e p a r e s t h e r o o t o f V 7 o f F-s h a r p . The case f o r i t s i m p l i c i t p r e s e n c e i n measure 2 w i l l be s t r e n g t h e n e d when we ob s e r v e measures 13 and 20, i n which D a c t u a l l y o c c u r s w i t h t h e measure 2 c h o r d , l a t e r i n t h i s a n a l y s i s . A t p r e s e n t , i t r e s t s upon t h e l i s t e n e r ' s awareness, when h e a r i n g Example 4 .6 , o f t h e two i m p o r t a n t harmonic v o i c e m o t i o n s (Example 4 . ? ) , Example 4 .7 : J\ which c h a r a c t e r i z e t h e p r e p a r a t i o n o f a dominant by T S ( V 7 / v ) ; as l e v e l 3 o f Example 4.6 shows, t h e s e two harmonic v o i c e s s t r i v e t o ward t h e r o o t o f Vf o f F-sharp, whereas a l l o f t h e o t h e r v o i c e s e n t e r and r e m a i n upon p i t c h e s o f t h a t V 7 c h o r d , a n t i c i p a t i n g i t s u l t i m a t e a r r i v a l i n measure 5« T h i s r e s u l t s i n t h e a r p e g g i a t i o n o f V 7 o f F-sharp (from E-sharp/F t h r o u g h G-sharp t o C-sharp) which we see c l e a r l y i n Example 4 .6 , l e v e l s 2 and 3i and which urges us t o s i m p l i f y measures 1 to 5 f u r t h e r i n o r d e r t o emphasize t h e f u n c t i o n V 7 o f F-sharp. T h i s i s done i n Example 4 . 8 , w h i c h e l i m i n a t e s t h e TS(V 7/V) f u n c t i o n i n f a v o r o f t h e p r e m a t u r e l y - a r r i v i n g p i t c h e s o f V 7 which oppose i t . Example 4 . 8 : F#: i i i — v i i We may now i n t e r p r e t t h e d i m i n i s h e d t r i a d , B - D - F, which a r o s e from t h e i n i t i a l B - f l a t minor harmony o f measure 1 as t h e f i r s t i n d i c a t i o n o f v i i 0 7 i n F-sharp which becomes V 7 when D moves t o C - s h a r p / D - f l a t i n measures 4 and 5- We now f i n d t h a t i t m a t t e r s l i t t l e whether the measure 2 c h o r d i s i n t e r p r e t e d as an E major t r i a d ( w i t h an i m p l i e d minor 07 s e v e n t h , D - n a t u r a l , from measure 1) o r s i m p l y as v i i ' o f F-7 s h a r p : t h e f o r m e r c h o r d would f u n c t i o n as V o f t h e r e l a t i v e k ey t o F-sharp (A), t u r n i n g d i r e c t l y t o V 7 o f F-sharp w i t h t h e " m i n o r - t h i r d c o n n e c t i o n " o f s e v e n t h chords d i s c u s s e d i n C h a p t e r I (Example 4 . 9 ) . S i n c e V 7 o f F-sharp and V 7 o f A s h a r e t h e same d i m i n i s h e d - s e v e n t h " a x i s " o f B - D - F/E-sharp 120 Example 4.9: F#: r e l a t i v e key, A G-sharp, Example 4.9 can be s a i d t o be j u s t as much concerned w i t h t h e dominant f u n c t i o n o f F-sharp as i s 4.8, o n l y t o r e -p r e s e n t a s l i g h t l y d i f f e r e n t p r e p a r a t i o n o f t h a t dominant, i n v o l v i n g a h i n t a t the m i n o r - t h i r d - r e l a t e d key o f A r e s u l t -The r o l e o f the p i t c h e s D - f l a t and F/E-sharp i n the f i r s t f i v e measures o f t h i s p i e c e i s now c l e a r : t h e y a r e t h e common ton e s between the i n i t i a l B - f l a t minor t r i a d and t h e g o a l c h o r d , C-sharp m a j o r - m i n o r - s e v e n t h , o f measure 5* Example 4.10 i s t h e f i n a l s i m p l i f i c a t i o n o f t h i s p o r t i o n o f t h e p i e c e , and i t shows t h a t t h e g o a l c h o r d i s b e i n g p r e p a r e d from th e v e r y f i r s t measure. I n measure 6, o u r e x p e c t a t i o n o f a r e s o l u t i o n t o F-s h a r p harmony i s f u r t h e r e d by t h e b r e a k i n g away o f a c h r o -n m a t i c a l l y d e s c e n d i n g l i n e from the r o o t o f V f which s t a t e s C-i n g from th e f l e x i b i l i t y o f v i i 121 Example 4.10: "m. "1 m. 1 5 n a t u r a l and G - f l a t ( o r B-sharp and B - n a t u r a l ) ; t h e e a r r e a c h e s f o r B - f l a t / A - s h a r p , b u t does n o t y e t f i n d i t (Example 4.11). m 5 6 3 E We do h e a r E-sharp/F s p l i t i n t o two harmonic v o i c e s , r e s o l v -i n g t o E - n a t u r a l and F-sharp i n measure 7, a f t e r t h e f a s h i o n o f a t y p i c a l l e a d i n g - t o n e which moves to t h e t o n i c and the i m m e d i a t e l y - g e n e r a t e d , l o w e r e d s e v e n t h o f the n e x t c h o r d a l o n g the c y c l e o f f i f t h s ( w i t h t h e d i f f e r e n c e t h a t t h e 122 l o w e r e d s e v e n t h , E, a c t u a l l y o c c u r s "before t h e t o n i c , F - s h a r p ) . T h i s r e s u l t s i n t h e b a r e s t h i n t o f l l ? 7 o r V / l V i n F-sharp w h i c h , i n t e r e s t i n g l y , does r e s o l v e i n t h e n e x t measure t o a b r i e f l y s u g g e s t e d IV (Example 4 . 1 2 ) . Example 4 . 1 2 : The h i n t o f V / l V and IV i n F-sharp, i n measures 7 and 8. /) PPP 3 . _ . G /F#: V 7 V 7 / I V IV ( i g n o r i n g C# p e d a l p o i n t ) Example 4 . 1 2 shows t h a t t h e r o l e o f t h e E - n a t u r a l and F-s h a r p o f measure 7 i n announcing t h e e n t r y o f t h e f i r s t v o c a l p h r a s e i s a p r o d u c t n o t o n l y o f t i m b r a l and r h y t h m i c d e v i c e s ( t h e d i s t i n c t i v e q u a l i t y o f t h e h i g h o c t a v e s and the t h r e e -b e a t d u r a t i o n o f F - s h a r p ) , b u t a l s o o f a c o h e r e n t t o n a l r e l a -t i o n s h i p . I n measure 8, we f i n d t h a t a t t r i b u t i n g the subdom-i n a n t f u n c t i o n t o t h e b e g i n n i n g o f t h e v o c a l p h r a s e was essen-t i a l l y c o r r e c t : the music from t h e b e g i n n i n g o f measure 8 to t h e end o f b e a t 1 i n measure 9 c o n s t i t u t e s an attempt t o r e a c h an F-sharp ^ c h o r d by means o f t h e t r a d i t i o n a l , embel-l i s h i n g p r o g r e s s i o n , i i 7 - # i i 7 - 1^, t h i s b e i n g e n t i r e l y 123 c o m p a t i b l e w i t h t h e i n i t i a l sense o f subdominant harmony i n measure 8. Example 4.13 shows th e approach t o an i m p l i e d 1^  i n F - s h a r p ; i t a l s o shows t h a t t h e C-sharp p e d a l - p o i n t may n be h e a r d t o combine w i t h t h e i i f u n c t i o n o f measure 8 t o 11 7 s u g g e s t V ^ , i n v i e w o f t h e emphasis a l r e a d y p l a c e d upon V o f F-sharp i n measures 5 and 6. Example 4.13: Als wir hin-ter dem be - bliiin - ten Tc 'o Nous a - vions fran-chi To la por-te fleu - ri 8 G |?/F#: IV ( u n t i l - - i i 7 ~ - — - # - — - - „" I A H o v e r C# p e d a l - p o i n t - — ( i f ) G|?/F#: i i 7 # i i 7 o r ( w i t h t h e C#, v i i o ? / V V 9 - 1 1 suggested) •<I$> 124 From Example 4.13, a s i m i l a r i t y between measures 8 and 1 i s d i s c e r n i b l e . I n b o t h measures, th e r o o t and t h i r d o f a m i n o r t r i a d a r e r a i s e d by s e m i tones t o c r e a t e d i m i n i s h e d t r i a d s . T h i s comparison draws a t t e n t i o n t o t h e f a c t t h a t a s t e p backward a l o n g t h e c y c l e o f f i f t h s i n F-sharp has t a k e n p l a c e s i n c e t h e b e g i n n i n g o f the p i e c e : whereas i n measure 1, t h e d i m i n i s h e d t r i a d , B - D - F, was s u g g e s t i v e o7 o f v i i ' o f F-sharp, i n measure 8, the p i t c h e s A, C, and E-f l a t p a r t i c i p a t e i n v i i f/V i n F-sharp,,(Example 4.14). I n Example 4.14: M i n o r t r i a d s moving t o d i m i n i s h e d t r i a d s i n measures 1 and 8, r e s u l t i n g i n the f u n c t i o n s viio7 and viio7/V i n F - s h a r p , r e s p e c t i v e l y . . Measure 1: - Measure 8 ( v o c a l l i n e ) : ( p a r t i a l ) ( p a r t i a l ) f a c t , measures 8 t h r o u g h 12 d e a l e s s e n t i a l l y w i t h d i f f e r e n t e x p r e s s i o n s o f pre-dominant harmony i n F-sharp which o n l y b r i e f l y b r i n g i n t h e dominant i n measure 11, b e f o r e d e p a r t i n g from i t i m m e d i a t e l y . Pre-dominant harmony i s e x p r e s s e d i n t h e forms o f V 7/V, T S ( V 7 / v ) , and t h e a l r e a d y - m e n t i o n e d v i i 0 7 , a l l o f which appear i n t h e s k e t c h o f measures 8 t o 12 i n Example 4.15, page 125. T h i s example w a r r a n t s a s t e p - b y - s t e p e x p l a n a t i o n as a g r e a t d e a l o f harmonic o v e r s t a t e m e n t t a k e s p l a c e w i t h i n i t ; f o r t h i s p u r p o s e , l e t t e r s from (a) t o (k) have been p l a c e d below t h e harmonic s t r u c t u r e s . S t r u c t u r e s 125 126 Example 4.15» c o n t i n u e d . if 7 7 'ft f p * c w a r den uns er - dach -dsais - tu, pro . mes ( i ) ( i ) ( j ) (a) and (b) have a l r e a d y been d i s c u s s e d i n Example 4.13; i n t h a t example, (b) was d e s c r i b e d as a d e c o r a t i v e - " # i i 7 " o f an i m p l i e d t o n i c harmony i n F-sharp, w i t h the p r o v i s o t h a t i t has t h e p o t e n t i a l t o be h e a r d as v i i o 7 / v i n F-sharp. Indeed, the l a t t e r f u n c t i o n i s c l e a r when we l o o k t o the f i r s t q u a r t e r o f measure 11, which i s r e p r e s e n t e d by s t r u c t u r e ( i ) o f Example.4.15 on page 126; however, t h e i n t e r i m s t r u c t u r e s a r e i n t r i g u i n g . S t r u c t u r e s ( c ) and (d) are i n f e r r e d from t h e segment o f t h e v o c a l l i n e (Example 4.16), 127 Example 4.16: . ----- —, w h i c h , p l a y e d out o f c o n t e x t , s u g g e s t s m o t i o n a l o n g the c y c l e o f f i f t h s from pre-dominant t o dominant harmony i n e i t h e r F-s h a r p o r C, as shown i n Example 4.17, and r e c a l l s t h e l e f t -hand p o r t i o n o f t h e p i a n o accompaniment i n measures 2 t o 5 (Example 4.18). Example 4.17: $Vv^ teH- 1^  Of* ' F#: TS(V 7 /v) V 7 C: i i 7 — y 7 ' (D and C as d o u b l e - n e i g h b o r ) (D and C as m i n o r 7th) Example 4.18: P i a n o , l e f t hand o f measures 2 t o 5 m. u -t^>—5 • [Mr I n measures 2 t o 5» the s t a g e s o f harmonic f u n c t i o n were pre-dominant and dominant i n F - s h a r p ; t h e i n t e r v a l D - C was s a i d t o i m p l y t h e f u n c t i o n TS(V 7/V) ( a l t h o u g h t h e p r e -dominant t r i t o n e , C - G - f l a t / F - s h a r p , was n o t p r e s e n t ) , arid t h e i n t e r v a l B - F/E-sharp was s a i d to p a r t i c i p a t e i n the o7 f u n c t i o n v i i ' o f F-sharp. I n measure 9* e s s e n t i a l l y t h e same i n t e r p r e t a t i o n i s made: a g a i n , D - C s u g g e s t s t h e p r e -dominant s t a g e , c o n t i n u i n g from the i m m e d i a t e l y p r e c e d i n g v i i o 7 / V as would a t r a d i t i o n a l TS(V 7/V) save t h e s o u n d i n g o f F - n a t u r a l which c o u n t e r a c t s t h e o n g o i n g F-sharp p e d a l p o i n t . 128 T h i s i s shown i n the c l o s e - u p o f s t r u c t u r e s (b) and ( c ) i n Example 4 . 1 9 . As f o r t h e i n t e r v a l , B - F/E-sharp, i t i s s t i l l Example 4 . 1 9 s C l o s e - u p o f s t r u c t u r e s (b) and ( c ) . - is — : , • - 4 1 x ( b ) ( c ) ^ — t o ?? Udt*., fcr—7 .-•1 " " T 1 ^ — F#: V j i ° 7 — T S ( X Z ) [ v 7 o r vii° 7 ] V v h e a r d as i m p l y i n g t h e d i m i n i s h e d - s e v e n t h c h o r d , B - D - F - A-f l a t , shown as s t r u c t u r e (d) i n Example 4 . 1 5 ? however, th e 7 r e s o l u t i o n t o V o f F-sharp w h i c h o c c u r r e d i n measure 5 when D - n a t u r a l descended t o D - f l a t / C - s h a r p does n o t r e c u r i n meas-ur e 9 « I n s t e a d , t h e d i m i n i s h e d - s e v e n t h c h o r d , s t r u c t u r e ( d ) , behaves as an e m b e l l i s h m e n t o f V 7/V, s t r u c t u r e ( e ) . T h i s i s shown i n Example 4 . 2 0 , which i s a c l o s e - u p o f s t r u c t u r e s (d) and (e)). ? Example 4 . 2 0 : N o t i c e t h a t (cl) e m b e l l i s h e s (e) as would (b) o f Example 4 . 1 9 e m b e l l i s h a t o n i c c h o r d i n F-sharp. (d) (e) 129 S t r u c t u r e s ( f ) and (g) o f Example 4.15 are made t o appear more d i s t i n c t from one a n o t h e r t h a n i s a c t u a l l y t h e case i n t h e music, f o r as we hea r the f i n a l p i t c h o f t h e vo-c a l p h r a s e i n measure 10, E - n a t u r a l , which completes t h e f l e e t i n g l y h e a r d C major t r i a d , we a l s o h e a r t h e whole o f s t r u c t u r e ( g ) . The C major t r i a d i s s t a t e d s e p a r a t e l y , as s t r u c t u r e ( f ) , t o emphasize i t s r e l a t i o n s h i p t o s t r u c t u r e s ( c ) and ( d ) ; C l i e s a t r i t o n e away from the p r e v a i l i n g t o n i c , F - s h a r p , and i s t h e r e f o r e t h e prime c a n d i d a t e f o r one o f Schoenberg's h i n t s o f an a l t e r n a t e t o n i c , as t h e j u x t a p o s i t i o n o f s t r u c t u r e s ( c ) , ( d ) , and ( f ) s u g g e s t s (Example 4.21). Example 4.21: V Urn h - Wm ! /v> — n - — - ufcr» k. "\ i ^ — (;y ^d)J S t r u c t u r e s (g) t h r o u g h ( i ) were d e a l t w i t h when meas-u r e s 2 t o 5 were d i s c u s s e d (Examples 4.6 t o 4.10, pages 117-122). However, t h e i r t r e a t m e n t i n measures 10 and 11 d i f f e r s s l i g h t l y w i t h r e s p e c t t o t h e o r d e r i n g o f t h e s t r u c t u r e s i n t i m e . Whereas i n measures 2 t o 5 we h e a r d t h e o r d e r o f s t r u c -t u r e s as ( h ) , ( g ) , ( h ) , ( i ) , and e l i m i n a t e d t h e second (h) t o s i m p l i f y t h e a n a l y s i s , i n measures 10 and 11, we h e a r o n l y (g)» ( h ) , and ( i ) . F u r t h e r m o r e , t h e (g) and (h) o f measure 10 a r e made l e s s d i s t i n c t from one a n o t h e r by t h e pr e s e n c e o f E - n a t u r a l from t h e v o c a l l i n e i n ( g ) . S t i l l , s t r u c t u r e (g) r e p r e s e n t s a pre-dominant f u n c t i o n i n F-sharp, because o f the 130 i n t e r v a l D - C/B-sharp which i s so i m p o r t a n t t o t h e TS(V 7/V) f u n c t i o n ; t h i s f u n c t i o n i s s u g g e s t e d d e s p i t e t h e p r e s e n c e o f C-sharp and F/E-sharp i n t h e p i a n o t r e b l e , p i t c h e s which a n t i c i p a t e t h e subsequent dominant f u n c t i o n i n F-sharp. The i n f e r r e d G-sharp o f s t r u c t u r e (g) i s i n c l u d e d t o complete t h e p a t h o f t h e harmonic v o i c e which s t a t e d G - n a t u r a l i n s t r u c t u r e ( f ) ; t h i s i s a v a l i d a c t o f harmonic o v e r s t a t e m e n t s i n c e G-n a t u r a l may c e r t a i n l y n o t be h e a r d as s u s t a i n e d t h r o u g h s t r u c t u r e ( g ) , which i s a c o m b i n a t i o n o f t h e d o u b l e - n e i g h b o r p a i r , D - C/B-sharp, and a n t i c i p a t i o n s o f t h e C-sharp t r i a d t o which t h e p a i r w i l l p r o g r e s s i n measure 11. S t r u c t u r e ( h ) , as i n measures 2 t o 4, r e p r e s e n t s an e s s e n t i a l l y dominant f u n c t i o n i n F-sharp, a l t h o u g h , a s was p r e v i o u s l y shown i n Example 4.9 o f page 120, t h e r e e x i s t s a h i n t o f t h e dominant o f A as w e l l . A g a i n , D - n a t u r a l i s i n -c l u d e d as a p r o d u c t o f harmonic o v e r s t a t e m e n t , j u s t i f i e d by t h e f a c t t h a t t h e D - n a t u r a l o f s t r u c t u r e (g) must f a l l t o D - f l a t / C - s h a r p o f s t r u c t u r e ( i ) and may t h e r e f o r e be t h o u g h t t o r e m a i n i m p l i c i t l y t h r o u g h t h e i n t e r m e d i a t e s t r u c t u r e ( h ) . The p i t c h e s c o n t a i n e d i n t h e box drawn i n Example 4.15 a r e t h o s e which a r e t o become members o f s t r u c t u r e ( i ) , and which o c c u r e a r l i e r , a n t i c i p a t i n g t h e dominant f u n c t i o n i n F-s h a r p . T h i s means t h a t t h o s e p i t c h e s n o t i n c l u d e d i n the box which p a r t i c i p a t e i n s t r u c t u r e s (g) and (h) p r o v i d e us w i t h a c o n c i s e summary o f t h e harmonic v o i c e a c t i v i t y which a c t u a l l y p r o g r e s s e s t o t h e dominant. We can d i s c e r n two t w o - v o i c e d p r o c e s s e s , o c c u r r i n g s i m u l t a n e o u s l y , which p r o v i d e a s t r i k i n g t e s t i m o n y t o t h e i m p o r t a n c e o f two c o n c e p t s i n t r o d u c e d i n 131 C h a p t e r I I as fundamental t o Schoenberg's harmonic l a n g u a g e : t h e e x p a n s i o n o f a d o u b l e - n e i g h b o r p a i r (augmented s i x t h ) t o an o c t a v e , and t h e c o n t r a c t i o n o f a minor s e v e n t h t o a minor s i x t h which s u g g e s t s m o t i o n between m i n o r - t h i r d - r e l a t e d dom-i n a n t - s e v e n t h chords (Example 4.22). Example 4.22: From s t r u c t u r e - : Cg) (h) ( I ) "Harmonic v o i c e p r o t o t y p e From s t r u c t u r e : (g) (h) ( i ) Harmonic v o i c e p r o t o t y p e S t r u c t u r e ( i ) o f Example 4.15, t h e dominant-seventh o f t h e i m p l i e d t o n i c , F-sharp, s t i l l does n o t a c h i e v e a r e s o l u -t i o n , a l t h o u g h w i t h s t r u c t u r e (k) we r e c e i v e a vague h i n t o f one. P r o c e e d i n g i n d e t a i l from the b e g i n n i n g o f measure 11, we f i n d t h a t s t r u c t u r e ( i ) i s p r o l o n g e d f o r t h e measure, w i t h n e i g h b o r - t o n e m o t i o n from the i n f e r r e d f i f t h o f the c h o r d , G-s h a r p , t o A and back, and t h e e m b e l l i s h m e n t o f t h e s e v e n t h , B, w i t h i t s u p p e r - n e i g h b o r , C. S t r u c t u r e ( j ) i s a p r o d u c t o f harmonic o v e r s t a t e m e n t . 7 H a v i n g i n t e r p r e t e d t h e r o o t , t h i r d , and s e v e n t h o f V o f F-s h a r p as p r o l o n g e d u n t i l t h e end o f measure 11, we f i n d t h a t the s t r o n g m o t i o n from G-sharp t h r o u g h G - n a t u r a l t o F-sharp and C-sharp ( i n t h e p i a n o t r e b l e ) s u g g e s t s t h a t E-sharp/F i s 132 no l o n g e r p r e s e n t , b u t has r e s o l v e d as w e l l t o F-sharp, as i n d i c a t e d i n Example 4.15. S t r e t c h i n g t h e harmonic o v e r -s t a t e m e n t t o i t s l i m i t , we mi g h t a l s o sense t h a t B from s t r u c t u r e ( i ) f a l l s i m p l i c i t l y t o A ( o r A-sharp) w i t h t h e a r r i v a l o f s t r u c t u r e ( k ) , r e s u l t i n g i n t h e l a t t e r s t r u c t u r e ' s s u g g e s t i o n o f a momentary F-sharp ^ c h o r d . W i t h t h e appearance o f s t r u c t u r e ( k ) , the T S ( V 7 / V ) f u n c t i o n i s r e i n s t a t e d . We may i n f e r t h e pr e s e n c e o f F-sh a r p and A i n s t r u c t u r e ( k ) , h e l d o v e r from ( j ) . The D-sh a r p which becomes added t o s t r u c t u r e ( j ) c r e a t e s a l o c a l d o u b l e - n e i g h b o r e m b e l l i s h m e n t o f t h e subsequent D - n a t u r a l , s i n c e D-sharp i s h e a r d between two s t a t e m e n t s o f C-sharp i n the v o c a l l i n e . Measures 11 and 12 may be summarized by s t r u c t u r e s ( i ) and ( k) a l o n e , i f one f i n d s t h a t ( j ) i n v o l v e s too r a d i c a l an assum p t i o n o f harmonic o v e r s t a t e m e n t ; however, s t r u c t u r e ( j ) i s n e c e s s a r y i f one wishes t o be v e r y s p e c i f i c about t h e p a t h n o f e v e r y harmonic v o i c e o f V o f F-sharp and t o acco u n t f o r a l l o f t h e p i t c h e s i n t h e m u s i c . With t h e s l o w tempo o f t h e p i e c e , one can i n d e e d h e a r h i n t s o f the o v e r s t a t e d v e r s i o n o f measures 11 and 12 p r e s e n t e d i n Example 4.15« I n measure 13, an a l t e r e d r e c a p i t u l a t i o n o f measures 1 t o 5 b e g i n s . The same upper v o i c e which o c c u p i e d the p i a n o accompaniment i n t h o s e measures may be t r a c e d i n measures 13 t o 16, a l t h o u g h t h e harmonic p a c i n g and c o n t e n t d i f f e r i n the two passages (Example 4.23). D e s p i t e t h e s i m i l a r i t y o f melo-d i c c o n t o u r between measures 1 t o 5 and 13 t o 16, the harmonic p r o g r e s s i o n which o c c u r s d u r i n g t h e e a r l i e r passage i s r u s h e d 133 Example 4.23: M e l o d i c p a r a l l e l between measures 1-5 and 13-16. — ^4 2 If ! 1 # ^ 1 y*y w ; 13 14 15 16 i n t o two measures,13 and 14, a f t e r which B - f l a t minor harmony r e t u r n s and e n t i r e l y new harmonic e v e n t s f o l l o w . Example 4.24, page 134, p r e s e n t s a harmonic v o i c e summary o f measures 13 and 14. I n l e v e l 1, t h e r i g h t - and l e f t - h a n d p a r t s o f t h e p i a n o accompaniment have been b r o u g h t c l o s e r t o g e t h e r and th e harmonic s t r u c t u r e s which p a r a l l e l t h o s e o f measures 1 t o 5 have been c i r c l e d ? no attempt has been made on t h i s l e v e l t o show complete harmonic v o i c e s . The r i g h t - h a n d p o r t i o n o f th e accompaniment i n measure 14 has been s i m p l i f i e d i n t h e f o l l o w i n g way: t h e f i r s t h a l v e s o f t h e f i r s t t h r e e b e a t s o f the measure a r e i n t e r p r e t e d as e m b e l l i s h m e n t s o f t h e second h a l v e s , because t h e y i n v o l v e a r p e g g i a t e d " f o u r t h c h o r d s " whose d o u b l e - n e i g h b o r p a i r s e m b e l l i s h the p i t c h - c l a s s e s B, F, and B - f l a t , as shown i n Example 4.25 on page 135« The p a r a l l e l between measures 13 and 14 and 1 t o 5 must be d i s c u s s e d i n d e t a i l . The f i r s t s t r u c t u r e c i r c l e d on l e v e l 1 o f Example 4.24 i s t h e B - f l a t minor t r i a d which appears i n t h e p i a n o bass i n measure 13; t h i s c h o r d , o f c o u r s e , 134 135 Example 4.25s D o u b l e - n e i g h b o r " f o u r t h " chords i n t h e p i a n o t r e b l e o f measure;, 14,': e m b e l l i s h i n g B - F and B-f l a t s F. p a r a l l e l s t h a t f o u n d i n the p i a n o t r e b l e i n measure 1. The second s t r u c t u r e c i r c l e d , a t t h e end o f measure 13» p a r a l l e l s t h a t o f measure 2, w i t h the e x c e p t i o n t h a t an a c t u a l D - n a t u r a l i s now p r e s e n t where i t was o n l y i n f e r r e d i n measure 2. T h i s c h o r d i s shown t o be approached i n a r a t h e r complex way on l e v e l 2 o f Example 4.24: t h e p o r t i o n o f the c h o r d which i s an E m ajor t r i a d r e s u l t s most i m p o r t a n t l y from t h e harmonic v o i c e m o t i o n s from E - f l a t / D - s h a r p t o E and A t o A - f l a t / G -s h a r p which appear i n t h e v o c a l l i n e and the p i a n o t r e b l e , r e s p e c t i v e l y ; i n a d d i t i o n t o t h e s e m o t i o n s , B i s approached by B - f l a t i n the p i a n o t r e b l e , and t h e G o f t h e v o c a l l i n e may be h e a r d as t h e l o w e r n e i g h b o r o f G - s h a r p / A - f l a t o f the p i a n o t r e b l e ; f i n a l l y , t h e C - n a t u r a l o f the v o c a l l i n e may be i n t e r p r e t e d as c a n c e l l e d out once B - n a t u r a l o c c u r s . A l l o f t h e s e m o t i o n s , o c c u r r i n g s i m u l t a n e o u s l y , r e s u l t i n the two 136 t h r e e - v o i c e d s t r u c t u r e s shown i n the v o c a l and t r e b l e p i a n o s t a v e s o f l e v e l 2, Example 4.24. The r e m a i n i n g p i t c h e s o f t h e c h o r d i n q u e s t i o n , D and F i n t h e p i a n o b a s s , stem from t h e i n i t i a l B - f l a t m i n o r t r i a d o f measure 13' As i n measure 1, D - f l a t r i s e s t o D - n a t u r a l and B - f l a t i s l e s s d i r e c t l y -r e p l a c e d by B - n a t u r a l . ( B - f l a t and B - n a t u r a l are t h e f i r s t and f i n a l p i t c h e s , r e s p e c t i v e l y , o f measure 13») The impor-t a n t d i f f e r e n c e between measure 13 and measures 1-2, t h a t t h e l a t e r measure i s a compressed v e r s i o n o f t h e harmonic e v e n t s o f t h e e a r l i e r two, i s v i t a l t o t h e case made f o r t h e i m p l i c i t p r e s e n c e o f D - n a t u r a l i n t h e measure 2 c h o r d (page 1 1 8 ) i i n measure 13» one a c t u a l l y h e a r s t h e measure 2 c h o r d e n t e r i n g w h i l e D - n a t u r a l i s s t i l l s o u n d i n g . We w i l l f i n d s i m i l i a r c i r c u m s t a n c e s l a t e r , i n measure 20. The t h i r d s t r u c t u r e c i r c l e d on l e v e l 1 o f Example 4.24 i s e s s e n t i a l l y a C-sharp m i n o r - s e v e n t h c h o r d w i t h b o t h major and m i n o r t h i r d , o r t h e same c h o r d as was j u s t h e a r d , save t h e l o w e r i n g o f D - n a t u r a l t o C-sharp. T h i s s t r u c t u r e does n o t q u i t e c o r r e s p o n d t o t h e C-sharp m a j o r - m i n o r - s e v e n t h c h o r d o f measure 5; i t seems, r a t h e r , t o combine t h a t c h o r d w i t h t h e measure 2 c h o r d , by i n c l u d i n g E - n a t u r a l . T h i s s u g g e s t s a compression o f t h e e v e n t s from measure 2 t o measure 5» o m i t t i n g the h i n t o f TS(Y7/V) which was h e a r d i n measure 3. As i n measures 1 t o 5» we may say t h a t t h e most im-p o r t a n t harmonic v o i c e motion' i n measures 13 and 14 i s t h a t from t h e B - f l a t i n t r o d u c e d as t h e r o o t o f a m i n o r t r i a d t o t h e B - n a t u r a l which becomes the s e v e n t h o f a c h o r d which i s 137 p o t e n t i a l l y V 7 o f F-sharp. The importance o f t h e t r i t o n e , B -F/E-sharp, i n the l a s t h a l f o f measure 13 and t h e f i r s t h a l f o f 14 i s c l e a r , as i s t h e common-tone r e l a t i o n s h i p between the D - f l a t from t h e B - f l a t minor t r i a d b e g i n n i n g measure 13 and t h e C-sharp o f the C-sharp minor t r i a d i n t h e n e x t meas-u r e . Example 4.10 o f page 121 i s r e p r o d u c e d as Example 4.26, as i t s e r v e s a l s o t o summarize measure 13 and t h e f i r s t h a l f o f 14. Example 4.26: We must c o n s i d e r an i m p o r t a n t , m o t i v i c m a t t e r from the b e g i n n i n g o f measure 1 3 — t h a t o f t h e now f a m i l i a r r a i s i n g , by s e m i t o n e s , o f t h e r o o t s and t h i r d s o f minor t r i a d s t o form d i m i n i s h e d ones. I n a d d i t i o n t o t h e r e l a t e d o c c u r r e n c e s o f t h i s harmonic event i n measures 1 and 13, which have j u s t been d e a l t w i t h , t h e same event was p r e s e n t e d i n the v o c a l l i n e o f measure 8, b e g i n n i n g from an A - f l a t minor t r i a d . Now, i n measures 13 and 14, we f i n d s e v e r a l minor t r i a d s , a l l o f which e x h i b i t t h e tendency t o become d i m i n i s h e d t h rough r a i s i n g o f t h e i r r o o t s and t h i r d s . E x a m i n a t i o n o f the v o c a l l i n e a l o n e i n t h e s e measures y i e l d s t h e "minor t o d i m i n i s h e d " p a t t e r n , o c c u r r i n g i n a c h a i n - l i k e f a s h i o n which l a s t s a lmost two complete segments (Example 4.27). 138 Example 4.27s 1^ .—1.3 minor I F F ..minor.. ( d i m i n i s h e d ? ) ToimThis n^ H Of c o u r s e , t h e manner i n which t h e v o i c e p r e s e n t s the t r i a d s emphasizes t h e minor ones on C and C-sharp; how-e v e r , i t i s i n t e r e s t i n g t h a t we do h e a r the p i t c h e s o f t h e second d i m i n i s h e d t r i a d , D, F, and G-sharp, as v e r y i m p o r t a n t d u r i n g t h e second and t h i r d b e a t s o f measure 14. They p a r t i -c i p a t e i n a v a g u e l y h i n t e d B - f l a t m a j o r - m i n o r - s e v e n t h c h o r d when, d u r i n g t h e second b e a t o f measure 14, harmonic v o i c e m o t i o n from B - n a t u r a l t o B - f l a t t a k e s p l a c e . But f o r t h i s m o t i o n , t h e d i m i n i s h e d - s e v e n t h c h o r d , B - D - F - G-sharp, i s p r o l o n g e d by s t a t e m e n t s o f t h e "minor t o d i m i n i s h e d " p a t t e r n on B - f l a t and C-sharp, as shown i n Example 4.28. Example 4.28: l.3_ 14 Moreover, t h e m i n o r - t h i r d r e l a t i o n s h i p o f m a j o r - m i n o r - s e v e n t h c h o r d s i n t r o d u c e d i n Chapter I I i s a g a i n a p p a r e n t ; r e f e r r i n g 139 now t o l e v e l 3 o f Example 4.24, page 134, we see t h a t , by-means o f t h i s m i n o r - t h i r d r e l a t i o n s h i p , Schoenberg r e t u r n s t o B - f l a t m i n o r harmony from t h e C - s h a r p - o r i e n t e d s t r u c t u r e a t t h e b e g i n n i n g o f measure 14. The h i n t o f a B - f l a t m a j o r - m i n o r - s e v e n t h c h o r d which p r e c e d e s t h e B - f l a t minor t r i a d a t t h e end o f measure 14 i s v e r y s i g n i f i c a n t i n v i e w o f t h e e v e n t s t o t a k e p l a c e i n measures 15 and 16. We f i n d t h a t a p r o g r e s s i o n a l o n g t h e c y c l e o f f i f t h s o c c u r s , moving t h r o u g h B - f l a t and E - f l a t s t r u c t u r e s t o c u l m i n a t e i n t h e a r r i v a l a t an A - f l a t s t r u c t u r e a t t h e b e g i n n i n g o f measure 16 which f u n c t i o n s as V / v i n F-s h a r p . T h i s p r o g r e s s i o n i s i n i t i a t e d i n measure 15 when the B - f l a t m i n o r t r i a d which b e g i n s t h a t measure becomes a major-m i n o r - s e v e n t h c h o r d i n e a r n e s t (we r e c a l l t h e h i n t i n t h e p r e c e d i n g measure which has j u s t been discussed?). The p r o -g r e s s i o n i s shown i n Example 4.29-L e v e l 1 o f Example 4.29 (page 140) shows which p i t c h e s p a r t i c i p a t e i n t h e p r o g r e s s i o n a l o n g t h e c y c l e o f f i f t h s , and how t h e y a r e i n t e r p r e t e d as a u r a l l y grouped t o g e t h e r : t h e f o u r main harmonic s t r u c t u r e s have been l a b e l l e d w i t h t h e l e t t e r s ( a ) , ( b ) , ( c ) , and (d) f o r e a s i e r r e f e r e n c e . L o o k i n g a t l e v e l 1, and t h e s c o r e above i t , one can see t h a t t h e D-n a t u r a l which makes s t r u c t u r e (b) a m a j o r - m i n o r - s e v e n t h c h o r d i s c o n s i d e r e d t o come from D - f l a t , t h e t h i r d o f t h e B -f l a t m i n o r t r i a d l a b e l l e d ( a ) . The p a s t two o c c u r r e n c e s o f the B - f l a t minor t r i a d (measures 1 and 13) i n v o l v e d n o t o n l y t h i s r i s e from D - f l a t t o D - n a t u r a l , b u t a l s o harmonic v o i c e m o t i o n from B - f l a t t o B - n a t u r a l which was o b s c u r e d by r e g i s t r a l 140 Example 4.29: P r o g r e s s i o n a l o n g t h e c y c l e o f f i f t h s i n measures. 15 and 16. L e v e l ~*'2T —Ht* , J t J = r | ¥= IMLBS — | 3? r b 5 z -^bii— - 1 | 13—12? hr (a) -fbf (d-141 d i s c r e p a n c i e s between th e B - f l a t and B - n a t u r a l ; i n t h i s c a s e , B - f l a t shows no s i g n - w h a t s o e v e r o f moving t o B - n a t u r a l , b u t r a t h e r , appears t w i c e i i n t h e t h i r t y - s e c o n d n o t e p a t t e r n o f t h e p i a n o accompaniment. The p e r f e c t f i f t h , B - f l a t - F, i s s t r o n g r i g h t up u n t i l s t r u c t u r e ( c ) a r r i v e s , so we do n o t h e a r , as i n measures 1 and 1 3 , the s u g g e s t i o n o f a dominant-s e v e n t h c h o r d i n F-sharp, which depends upon the t r i t o n e , B - n a t u r a l - F. S t r u c t u r e ( c ) i s s p e c i a l i n t h a t i t s u g g e s t s two harmonic f u n c t i o n s . The f i r s t i s a c h o r d on an E - f l a t b a s s , which would be "pre-pre-dominant" i n F-sharp. To make s t r u c t u r e ( c ) i n t o a c o n v e n t i o n a l v e r s i o n o f an E - f l a t c h o r d , we must i n f e r a G - f l a t o r n a t u r a l (and p o s s i b l y a D - f l a t ) as shown i n Example 4 . 3 0 . We j u s t i f y t h i s i n f e r e n c e o f G - f l a t o r n a t u r a l by assuming t h a t t h e s e v e n t h o f s t r u c t u r e ( b ) , A - f l a t / G = s h a r p , would n o r m a l l y t e n d t o f a l l t o one o f t h o s e p i t c h e s . The v e r s i o n o f s t r u c t u r e s (a) to (d) shown i n Example 4 . 3 0 i s s u p p o r t e d by t h e bass l i n e o f the accompani-ment, which moves o v e r t l y i n p e r f e c t f i f t h s from B - f l a t , t h r o u g h E - f l a t , t o A - f l a t , e m b e l l i s h i n g each o f t h o s e p i t c h e s w i t h i t s own dominant. However, i f we f o c u s our a t t e n t i o n upon th e n o t e s o f t h e p i a n o t r e b l e , we a r e encouraged t o l o o k a t s t r u c t u r e ( c ) q u i t e d i f f e r e n t l y . The u n d e r s t a n d i n g o f s t r u c t u r e ( c ) as an E - f l a t c h o r d r e q u i r e d i n t e r p r e t i n g t h e p i t c h e s F, A, and C o f the p i a n o t r e b l e as p a s s i n g tones t o t h e s e v e n t h , n i n t h and e l e v e n t h o f t h e subsequent V7/V c h o r d ; however, i n terms o f a c t u a l p i t c h - c l a s s c o n t e n t , s t r u c t u r e ( c ) i s s u r e l y a dominant-142 Example 4.30: (a) (b) * * ( c ) * * (d) s e v e n t h c h o r d i n r e l a t i o n t o t h e p r e c e d i n g B - f l a t s t r u c t u r e s , (a) and (t>). Example 4.31, t h e n , s u g g e s t s an i n t e r p r e t a t i o n o f measures 15 and 16 which i g n o r e s t h e emphasis p l a c e d upon E - f l a t i n t h e bass o f s t r u c t u r e ( c ) i n f a v o r o f a more l i t e r a l approach r e l y i n g upon p i t c h - c l a s s c o n t e n t . The v e r s i o n Example 4.31: (a) (b) ( c ) (d) shown i n Example 4.31 shows a m i n o r - t h i r d r e l a t i o n s h i p be-tween s t r u c t u r e s ( c ) and (d) r a t h e r t h a n a f i f t h r e l a t i o n s h i p . Measures 13 t o 16 were f i r s t i n t r o d u c e d , w i t h Example 4.23 o f page 133» as t h e m e l o d i c p a r a l l e l o f measures 1 t o 5. Now t h a t we have d e a l t w i t h the harmonic c o n t e n t o f b o t h pas-sages, we can compare the r e s p e c t i v e r o l e s o f t h e s i m i l a r upper v o i c e m e l o d i e s i n t h e i r d i f f e r e n t harmonic c o n t e x t s . T h i s i s done i n Example 4.32, page 143. We can see from t h i s example t h a t the p o i n t a t which t h e p o s i t i o n o f the m e l o d i e s i n t h e harmonic s t r u c t u r e s b e g i n s to d i f f e r i n the 143 Example 4.32: Beams show the p a r a l l e l m e l o d i e s . ~\ 2 3 If- ' 13 14 15 two passages i s i n measures 2 and 14; whereas G-sharp has a s t a b l e r o l e t h r o u g h o u t measure 2, as t h e t h i r d o f e i t h e r t h e vii° 7 o r ? V ' / r e l a t i v e key a s p e c t s o f the c h o r d i n Example 4.33. Example 4.33: G-sharp i n measure 14 g i v e s up t h a t r o l e t o become th e f i f t h o f a C - s h a r p - r o o t e d c h o r d ( t h e r o l e t a k e n by t h e G-sharp o f measure 5)t and goes on t o become th e s e v e n t h o f a B - f l a t m a j o r - m i n o r - s e v e n t h c h o r d . With the C-sharp s t r u c t u r e o f measure 14 comes th e c o m p l e t i o n o f the harmonic events which p a r a l l e l measures 1 t o 5; t h e B - f l a t c h o r d which f o l l o w s r e p r e s e n t s t h e b e g i n n i n g o f new harmonic e v e n t s , 144 a l t h o u g h t h e m e l o d i c e v e n t s p a r a l l e l t o measures 1 t o 5 occupy t h e music u n t i l measure 16. The most s t r i k i n g d i f f e r e n c e between any two r o l e s t a k e n by c o r r e s p o n d i n g m e l o d i c p i t c h e s i n t h e i r r e s p e c t i v e harmonic c o n t e x t s i s found where th e C - n a t u r a l o f measure 4 p a r a l l e l s t h a t o f measure 1$. I n the f o r m e r c a s e , C-n a t u r a l i s m e r e l y t h e l o w e r n e i g h b o r t o the C-sharp o f V i n F -sharp and i s f o r c e d t o sound w i t h i t s i n t e n d e d p i t c h o f r e s o l u t i o n . I n t h e l a t t e r c a s e , however, C - n a t u r a l i s more i m p o r t a n t thannC-sharp: a l t h o u g h C-sharp appears t o have r e t u r n e d a t the end o f measure 15, we f i n d t h a t C-n a t u r a l r e c u r s i n measure 16 and remains as a v i t a l p a r t o f t h e pre-dominant harmony i n measures 17 and 18 which l e a d s t o t h e dominant-seventh o f F-sharp i n measure 19• The C-s h a r p a t t h e end o f measure 15 p r o v e s t o be an upper n e i g h b o r t o t h e t h i r d o f V/V i n F-sharp, and behaves t r a d i t i o n a l l y , i n a 4-3 m o t i o n o v e r t h e A - f l a t / G - s h a r p r o o t . The e v e n t s which o c c u r from measure 16 t o measure 19 s e r v e t o p r o l o n g C - n a t u r a l as the l e a d i n g - t o n e t o C-sharp, p l a c i n g i t i n t h e c o n t e x t o f pre-dominant harmonic s t r u c t u r e s . We i m m e d i a t e l y h e a r t h e s i m i l a r i t y between t h i s passage and t h a t from measure 8 t o measure 12, which a l s o d e a l t w i t h p r e -dominant harmonic s t r u c t u r e s and f e a t u r e d C - n a t u r a l as a v e r y i m p o r t a n t p i t c h o f t h e v o c a l l i n e . The p r o l o n g a t i o n o f C - n a t u r a l i n measures 16 to 19 a c t u a l l y b e g i n s w i t h t h e s t a t e -ment o f t h a t p i t c h i n t h e m i d d l e o f measure 15/ From t h a t p o i n t on, C - n a t u r a l appears e v e r y measure i n t h e same o c t a v e and p a r t i c i p a t e s i n a most b a s i c pre-dominant s t r u c t u r e : t h e 145 d o u b l e - n e i g h b o r p a i r , D - C, which i s emphasized i n measures 16, 17, and 18, as shown i n Example 4.35 on page 146. The d o u b l e - n e i g h b o r p a i r s f o u n d i n t h e v o c a l l i n e are p a r t o f l a r g e r harmonic s t r u c t u r e s which f u n c t i o n as T S ( V 7 / V ) , as s k e t c h 1 o f Example 4.35 r e v e a l s . I n measure 16, TS( V 7 A ) i s h e a r d t o r e s o l v e v e r y b r i e f l y when t h e p i t c h e s E and C-sh a r p o c c u r , b u t i s i m m e d i a t e l y b r o u g h t back by t h e v o i c e ' s l e a p from D t o G o v e r t h e b a r - l i n e t o measure 1?. Measure 17 p r e s e n t s t h e complete whole-tone v e r s i o n o f T S ( V 7 / V ) ; "the p i t c h e s o f t h e v o c a l l i n e can be r e a r r a n g e d so t h a t t h e d o u b l e - n e i g h b o r p a i r , D - C, frames t h e whole-tone c o l l e c t i o n as i n Example 4.34. I n measure 18, TS(V 7/V) a g a i n d i s a p p e a r s f o r an i n s t a n t when we a r e g i v e n a h i n t o f t o n i c harmony, a f t e r which v i i o 7 / V and TS(V 7/V) b r i n g i n the V 7 o f measure 19. Example 4.34s The p i a n o accompaniment a l s o d i s p l a y s the dou b l e -n e i g h b o r p a i r , D - C, i n c o n t e x t o f pre-dominant harmonic s t r u c t u r e s . However, the t e r t i a n and whole-tone c h a r a c t e r o f t h e v o c a l l i n e i s c o n t r a s t e d by t h e emphasis upon f o u r t h s i n t he accompaniment. The f o u r t h s a r i s e from the t h i r t y -second-note passage o f measure 15» i n which B - f l a t , E - f l a t , and A - f l a t were e m b e l l i s h e d from below w i t h t h e i r dominants. Where the s k e t c h o f the p i a n o accompaniment i n Example 4.35 b e g i n s , we f i n d the f o u r t h E - f l a t - A - f l a t , which r e p r e s e n t s U6 147 V/V i n F - s h a r p . Immediately f o l l o w i n g i s the f o u r t h D - G, which r e p r e s e n t s the i n t e n s i f i c a t i o n o f t h a t pre-dominant f u n c t i o n and b r i n g s us one h a l f - s t e p c l o s e r to the g o a l p i t c h , C-sharp, c h a n g i n g the harmonic f u n c t i o n t o TS(V 7/V) when h e a r d i n c o n j u n c t i o n w i t h t h e v o c a l l i n e , which s u p p l i e s t h e n e c e s s a r y C. An a d d i t i o n a l harmonic i m p l i c a t i o n to t h o s e o f TS(V 7/V) and V found i n t h e v o c a l l i n e i n measure 16 a r i s e s from the emphasis upon G and the h i g h E-sharp i n the accompan-iment. G a l o n e would p r e s e n t us w i t h no c o m p l e x i t y , s i n c e i t c o u l d be s a i d to p a r t i c i p a t e i n the " f o u r t h t y p e " o f double-n e i g h b o r c h o r d ( i n t r o d u c e d i n C h a p t e r I I ) , D - G - C, which f u n c t i o n s as TS(V 7/V) i n F-sharp; however the p r e s e n c e o f E-s h a r p w i t h G i n the p i a n o t h r o u g h o u t most o f measure 16, and t h e c o n s p i c u o u s r e s o l u t i o n o f E-sharp t o F-sharp forms a new d o u b l e - n e i g h b o r c o m p l e x — G - E-sharp t o F-sharp. T h i s com-p l e x i s n o t a t a l l i n c o m p a t i b l e w i t h t h e p r e v i o u s l y d i s c u s s e d one o f D - C t o C-sharp; i n f a c t , i t s i m p l y c r e a t e s t h e im-p r e s s i o n o f a suspended f o u r t h (Example 4.36) when h e a r d w i t h t h e v o c a l l i n e ' s TS(V 7 / V ) and V s t r u c t u r e s , which i n c r e a s e s one's e x p e c t a t i o n o f the t h i r d , E - sharp. I n t h e s k e t c h o f the accompaniment i n Example 4.35» t h e d o u b l e - n e i g h b o r p a i r s D - C and G - E-sharp are shown to r e s o l v e s i m u l t a n e o u s l y t o C-sharp and F-sharp. Whereas we c o u l d now e x p e c t a 4-3 r e s o l u t i o n t o E-sharp and a complete V f s t r u c t u r e , t h i s does n o t o c c u r : i n s t e a d , the v o c a l p a r t makes a l e a p from D t o C, and when t h i s i s h e a r d w i t h t h e s t i l l - s o u n d i n g , h i g h F-sharp o f t h e accompaniment, TS(V 7/V) 148 Example 4.36: The e x p e c t a t i o n o f a "4-3" r e s o l u t i o n i n measures 16-17 . m be TO ben w i r -be-gan^ nen, ^/we&n 16 w i r ^ l e i s n u r an uns -3? (17) s e e * 2! ^ r e s u l t s . When t h e f o u r t h , G - C, o f t h e p i a n o accompaniment i n measure 17 o c c u r s , i t c o n t r i b u t e s i t s more important., upper p i t c h t o t h e TS(¥ 7/V) f u n c t i o n b e i n g e x p r e s s e d i n t h e v o c a l l i n e ; i n a d d i t i o n , i t forms the complete double-n e i g h b o r " f o u r t h " c h o r d , D - G - C, i f h e a r d as a c o n t i n u -a t i o n o f t h e f o u r t h , D - G, i n measure 16 o f the accompani-ment. A r g u i n g f o r t h i s a c c u m u l a t i o n o f f o u r t h s o v e r measures 16 and 17 i s t h e appearance o f E - f l a t and A - f l a t i n t h e l a t t e r measure. Whether o r n o t we can h e a r a l o n g - r a n g e r e l a t i o n s h i p between the D - G o f measure 16 and t h i s E - f l a t - A - f l a t , i t i s i n d i s p u t a b l e t h a t harmonic v o i c e m o t i o n from t h e s t r o n g l y - e m p h a s i z e d D - n a t u r a l o f t h e v o c a l l i n e t o t h e E - f l a t t a k e s p l a c e . F u r t h e r m o r e , the v o c a l l i n e s t a t e s C - f l a t s i m u l t a n e o u s l y w i t h t h e f o u r t h , E - f l a t -A - f l a t , i n the p i a n o , g i v i n g one t h e sense t h a t T S ( V 7 / v ) , which has o c c u p i e d measure 17 t h u s f a r , has r e g r e s s e d t o a s u p e r t o n i c t r i a d as shown i n Example 4.37. The r e g r e s s i o n t o i i shown i n Example 4.37 i s , o f 149 c o u r s e , i m m e d i a t e l y r e v e r s e d i n measure 18: i n t h i s measure, the p i a n o accompaniment q u i c k l y r e i n s t a t e s t h e double-n e i g h b o r p a i r , D - C, and goes on t o s t a t e t h e c h o r d (Example 4.38) Example 4.38: > '• 7 w h i c h , as p r e v i o u s l y , a n t i c i p a t e s the a r r i v a l o f V o f F-o7 s h a r p by i t s s i m i l a r i t y t o v i i 'min t h a t key. The v o c a l l i n e i s l e s s h a s t y , d w e l l i n g upon i t s pre-dominant p i t c h e s u n t i l t h e t r u e a r r i v a l o f V' o f F-sharp i n measure 19• The f i n a l t h r e e p i t c h e s o f t h i s v o c a l p h r a s e summarize what has been a three-measure p r e o c c u p a t i o n w i t h t h e d o u b l e - n e i g h b o r p a i r D - C and i t s f u n c t i o n , T S ( V 7 / V ) . We may compare measures 16 t o 19 w i t h t h e p r o t o t y p i c a l dominant approach shown i n Example 4.39, 7 The t r u l y u n u s u a l a s p e c t o f the music from the V c h o r d o f measure 19 on i s t h a t t h e dominant-seventh o f F-150 3 Example 4.39* Approach t o dominant-seventh o f F-s h a r p , comparable to e v e n t s i n measures 16 t o 19. Analogous t o : 16 1? 18 19 s h a r p , which we have s u p p o s e d l y been a w a i t i n g s i n c e measure 15 p r e s e n t e d V 7 / v , i s n o t t r e a t e d as a g o a l c h o r d by Schoenberg; r a t h e r , he uses i t t o l e a d i n t o measure 20, where th e c h o r d shown as Example 4.40 Example 4.40: /~ ~(V ] a p p e a r s . Whereas th e dominant-seventh o f F-sharp i n measure 19 o c c u r r e d on an o f f - b e a t , the measure 20 c h o r d o c c u r s on b e a t one; whereas t h e dominant-seventh c h o r d l a s t e d two and o n e - h a l f b e a t s , t h e c h o r d o f measure 20 l a s t s seven. Such f a c t s o b s c u r e t h e e f f e c t which t h e dominant-seventh might have as a t r u e g o a l c h o r d . H a r m o n i c a l l y , what was a c h i e v e d i n measure 19 i s now c l o u d e d ; however, the measure 20 c h o r d 0 7 s t i l l s u g g e s t s v i i ' o f F-sharp and a c r u c i a l a l t e r a t i o n i s made i n t h e s i x t e e n t h - n o t e r u n o f the p i a n o bass which f u r -t h e r s such an i n t e r p r e t a t i o n . We may show t h i s a l t e r a t i o n by p r e s e n t i n g t h e s i x t e e n t h - n o t e r u n as i t would be i f i t were an e x a c t t r a n s p o s i t i o n o f t h e o r i g i n a l r u n s t a t e d i n measure 1, and comparing t h i s v e r s i o n t o t h e r u n used by Schoenberg. T h i s i s done i n Example 4.41. 151 Example 4.41: H y p o t h e t i c a l and a c t u a l r u n s compared. —Hypo the t i c a i r u n Ac_tual_run , 7'q UJ j q ^ ^ iJ j" hj j H ^ The h y p o t h e t i c a l s i x t e e n t h - n o t e r u n shown i n Example 4.41 l a c k s one i m p o r t a n t f e a t u r e which i s p r e s e n t i n Schoenberg's a l t e r e d v e r s i o n i n measure 20: t h e r u n which Schoenberg uses ends on t h e l e a d i n g - t o n e t o F-sharp, and t h e r e b y h e l p s to m a i n t a i n the t r i t o n e o f t h e dominant-s e v e n t h c h o r d a c h i e v e d i n measure 19 u n t i l t h e m i d d l e o f measure 21. Schoenberg's r u n a l s o s e t s up the p i t c h e s o f 0 7 v i i ' o f F-sharp t o b e g i n the second and t h i r d groups o f s i x t e e n t h - n o t e s , so t h a t t h o s e p i t c h e s are n o t i c e d n o t o n l y because t h e y double the p i t c h e s c o n t a i n e d i n t h e measure 20 c h o r d , but a l s o because t h e y o c c u r a t p o i n t s o f s l i g h t r h y t h m i c emphasis i n t h e r u n . Example 4.42 p r e s e n t s an i n t e r p r e t a t i o n o f measures 20 and 21 which shows how the s i x t e e n t h - n o t e r u n p r o l o n g s a dominant f u n c t i o n i n F-sharp. I n Example 4.42, p i t c h e s p r e s e n t i n t h e measure 20 c h o r d a r e shown t o be a u r a l l y a c c u m u l a t e d as we h e a r t h e s i x t e e n t h - n o t e r u n . These p i t c h e s , G-sharp, D - n a t u r a l , and F - n a t u r a l , a l l o c c u r a t c o n s p i c u o u s p o i n t s i n the r u n . G-s h a r p f i r s t o c c u r s a f t e r t h e s u s t a i n e d upper n e i g h b o r , A-152 Example 4.42: , n a t u r a l , and i s s t a t e d f o r the second t i m e , an o c t a v e l o w e r , on the f i r s t b e a t o f measure 21s D - n a t u r a l o c c u r s on b e a t f o u r o f measure 20, and a g a i n as the l o w e s t p i t c h o f t h e r u n i n measure 21j F - n a t u r a l i s t h e f i n a l p i t c h o f t h e r u n . These p i t c h e s , when h e a r d w i t h the s u s t a i n e d B - n a t u r a l i n the p i a n o t r e b l e and the C - f l a t o f the v o c a l l i n e , f u n c t i o n as v i i ° 7 o f F-sharp. o7 Schoenberg s u g g e s t s the r e s o l u t i o n o f v i i ' t o I i n measure 21, where the v o c a l l i n e descends from C - f l a t t o B-f l a t j u s t a f t e r t h e l o w F - n a t u r a l o f t h e p i a n o bass has 153 moved to F-sharp, as shown i n Example 4.43. However, the B-Example 4.43 from end of run f l a t i s so momentary that when i t proceeds to A - f l a t and E-f l a t , we forge.t i t i n favor of the A - f l a t minor t r i a d formed by those pitches and the preceding G - f l a t s . As i n measures 8 and 9, the A - f l a t minor t r i a d functions as i i i n F-sharp; the presence of F-sharp and G-sharp i n the piano anticipate the tonic function which could occur i f the i i chord behaved i n one of the two common ways shown i n Example 4.44. We f i n d , upon l i s t e n i n g to the l a s t four measures of the piece, that Example 4.44(a) f a i r l y accurately represents the musical events which occur. However, a more detailed study of these f i n a l measures i s i n order; i t w i l l depict the exact path of each harmonic voice which operates i n measures 21 to 24. The reader should r e f e r to Example 4.45 during the following discussion (page 1 5 5 ) ' Level 1 of Example 4.45 harmonically overstates the l a s t four measures of the piece. The i n i t i a l sonority of that l e v e l i s comprised of the B-natural/C-flat of the vocal l i n e , the chord B - E - G-sharp of the piano treble, and the f i n a l three pitches of the sixteenth-note run i n the piano 154 Example 4.44: (1) The embellishment of I by i i 7 and # i i 7 , as i n measures 8 and 9» •tr. (2) The t r a d i t i o n a l cadence along the cycle of f i f t h s . bass (D, F, and G-sharp) as well as the implied pitches, D-natural and G-sharp, which were accumulated i n the course of the sixteenth-note run i n the preceding measure. When the tri t o n e , E-sharp - B, contracts to F-sharp and A-sharp on the t h i r d beat of measure 21, the harmonic overstatement depicts, implied motions i n other harmonic voices: D-natural i s shown to pass to C-sharp, although the l a t t e r pitch only occurs on beat four of the measure and does so four and f i v e octaves away; E-natural i s shown to move to D-sharp, which occurs on the l a s t h a l f of beat two i n the vocal l i n e , a l -though the former pitch actually remains u n t i l beat four (the E-natural occurred more than four beats ago. and has received no reinforcement through additional occurrences 155 Example 4 . 4 5 : Harmonic v o i c e summary o f measures 2 1 - 2 4 . mm u w a> j > j ^ b j 1 n So Que ver - blie-best du m i r l a n g ta pre - sence e - tait forte z u Sei et dou ten. 21 25= s i n c e t h e n , whereas D-sharp i s c l e a r l y a v e r y i m p o r t a n t p i t c h i n t h e v o c a l l i n e and i s s t a t e d i n the same o c t a v e as t h e f a d i n g E - n a t u r a l so as t o d e t r a c t from i t i n t h e s t r o n g e s t way p o s s i b l e ) . These harmonic v o i c e m o t i o n s , 156 b o t h r e a l and i m p l i e d , r e s u l t i n t h e second s o n o r i t y shown on l e v e l 1 o f Example 4.45- The o n l y harmonic v o i c e m o tions which t a k e p l a c e from t h i s p o i n t on a r e those from B - n a t u r a l t o B-sharp and G-sharp to G-double-sharp; D-sharp i s shown t o r e m a i n i m p l i c i t l y t h r o u g h o u t measures 22 and 23 as t h e f i f t h o f t h e s u p e r t o n i c - s e v e n t h s t r u c t u r e w i t h r a i s e d r o o t and t h i r d . L e v e l 2 o f Example 4.45 e l i m i n a t e s a l l o c t a v e d o u b l i n g s and s i m p l i f i e s the music r e g i s t r a l l y , as i n comparable r e d u c t i o n s t h r o u g h o u t t h i s s t u d y . The i n f e r r e d r e s o l u t i o n o f B-sharp to C-sharp and t h a t o f G-double-sharp t o A-sharp complete t h e t o n i c t r i a d by i m p l i c a t i o n . 157 CONCLUSION The a n a l y s e s o f Opus 15» Number 5 and Number 11, p r e s e n t e d i n c h a p t e r s I I I and IV are i n t e n d e d t o c o n t r i b u t e t o the u n d e r s t a n d i n g o f Schoenberg's music i n two ways: f i r s t , t h e y attempt to demonstrate t h a t c e r t a i n fundamental p r o c e s s e s o f t o n a l c o u n t e r p o i n t , p a r t i c u l a r l y as t h e y o p e r a t e i n n i n e t e e n t h - c e n t u r y harmonic c o n t e x t s , are a b a s i s f o r t h e t o n a l coherence s t i l l p e r c e i v e d i n Opus 15; second, the a n a l y s e s s e r v e as c o n c r e t e examples o f a p r a c t i c a l a n a l y t i c a l "method", i n v o l v i n g the concept o f harmonic v o i c e , which makes the a f o r e m e n t i o n e d p r o c e s s e s r e a d i l y a p p a r e n t . I n C h a p t e r I I , s p e c i f i c ways i n which t h e s e p r o c e s s e s a r e f e l t t o u n d e r l y Schoenberg's music p r i o r t o and d u r i n g Opus 15 were i n t r o d u c e d under s e v e r a l s u b j e c t h e a d i n g s : "The T r i t o n e S u b s t i t u t e " , "The Minor-Seventh/Augmented-S i x t h P o t e n t i a l o f 'Whole-tone' Chords", and "Double-n e i g h b o r P a i r s i n 'Whole-tone' and Other C o n t e x t s " were a few such h e a d i n g s . However, a l l o f the t o p i c s d i s c u s s e d i n C h a p t e r I I seem to stem from a s i n g l e , most b a s i c c o n c e p t . I t i s t h e concept t h a t t h e r o o t o f a c h o r d need n o t be p r e s e n t f o r i t s f u n c t i o n t o be e f f e c t i v e , and t h a t t h e r o o t may be i n f e r r e d from t h e t r i t o n e which i s p e r c e i v e d to r e p r e s e n t t h e m a j o r - t h i r d and m i n o r - s e v e n t h o f the c h o r d . ( F u r t h e r t o t h i s concept i s t h e i d e a t h a t , i n the absence o f a t r i t o n e , a minor s e v e n t h o r augmented s i x t h may suggest a 158 harmonic f u n c t i o n o r i t s t r i t o n e s u b s t i t u t e . ) Such a concept r e s u l t s i n an e s s e n t i a l e q u a l i t y o f meaning between c h o r d p r o g r e s s i o n s which might once have been d i s t i n g u i s h e d from one a n o t h e r by the a d j e c t i v e s "harmonic" and " l i n e a r v , o r even " d i a t o n i c " and " c h r o m a t i c " . Example 5«0s Two " e q u i v a l e n t " p r o g r e s s i o n s a l o n g t h e c y c l e o f f i f t h s i n C. ."The r a m i f i c a t i o n s o f a concept o f harmony which a l l o w s t h e two p r o g r e s s i o n s shown i n Example 5.0 to be c o n s i d e r e d f u n c t i o n a l l y e q u a l harmonic motions a l o n g the c y c l e o f f i f t h s a r e extreme w i t h r e s p e c t t o t h e a n a l y s i s o f h i g h l y c h r o m a t i c , t o n a l l y f l u c t u a t i n g music. A u s e f u l o v e r -s i m p l i f i c a t i o n o r summary o f t h e s e r a m i f i c a t i o n s would be to say t h a t , w i t h the a d o p t i o n o f t h i s concept o f t r i t o n e -d e t e r m i n e d f u n c t i o n , many harmonic s t r u c t u r e s which p r e v i o u s -l y m ight have, been t o s s e d o f f as b e i n g o f p u r e l y l i n e a r o r i g i n , w i t h t h e r e f o r e a t t e n u a t e d f u n c t i o n a l meaning ( i . e . , t h e "meaning" commonly denoted by Roman n u m e r a l s ) , may now be c o n s i d e r e d as t r u l y "harmonic". Of c o u r s e , t h e concept o f harmonic v o i c e , and t h e development o f a n o t a t i o n a l system which emphasizes s t e p -w i s e m o t i o n s common t o p r o g r e s s i o n s which might o t h e r w i s e 159 be c o n s i d e r e d d i f f e r e n t i n terms o f t h e h a r m o n i c - v e r s u s -l i n e a r d i s t i n c t i o n was a n e c e s s a r y outgrowth o f the a u t h o r ' s b e l i e f t h a t , i n some sense, Schoenberg's music c o u l d be c o n s i d e r e d a p u r e l y harmonic m u s i c , and e x p l o r e d from t h a t s t a n d p o i n t w i t h i n t e r e s t i n g r e s u l t s . I t remains to be d e t e r m i n e d what f u r t h e r uses t h e harmonic v o i c e concept might have i n a n a l y s i s , and f o r which i d i o m s i t might be s u i t a b l e . W ith r e s p e c t t o the r e s t o f Opus 15, which c o u l d n o t be d e a l t w i t h i n a work o f t h i s narrow scope, t h e f o l l o w -i n g songs l e n d t hemselves e s p e c i a l l y w e l l t o t h e a n a l y t i c a l approach demonstrated i n t h i s s t u d y : numbers 2, 3i 4, 9> 10, 12, and 15* However, i t i s my o p i n i o n t h a t a l l o f Opus 15, and l a t e r works by Schoenberg, might be e x p l o r e d v a l u a b l y u s i n g t h e harmonic v o i c e c o n c e p t . 1 6 0 FOOTNOTES "''Arnold Schoenberg, Theory o f Harmony, t r a n s . Roy E. C a r t e r (Los A n g e l e s : U n i v e r s i t y o f C a l i f o r n i a P r e s s , 1 9 7 8 ) , pp. 3 9 1 - 2 . 2 I b i d . , p. 3 9 2 . 3 I b i d . , p. 404. ^ I b i d . , p. 4 0 5 . ^Thomas C l i f t o n mentions Schoenberg's use o f key a r e a s a semitone a p a r t , r e f e r r i n g t o i t as the "semitone r e l a t i o n " i n h i s d i s s e r t a t i o n , "Types o f a m b i g u i t y i n Schoenberg's t o n a l c o m p o s i t i o n s " (Ph.D. d i s s e r t a t i o n , S t a n f o r d U n i v e r s i t y , 1 9 6 6 ) , p. 8 . ^ D a v i d L e w in p o i n t s o ut t h i s p a t t e r n o f major t h i r d s i n h i s a r t i c a l , "Toward t h e A n a l y s i s o f a Schoenberg Song," P e r s p e c t i v e s o f New Music ( F a l l - W i n t e r l 9 7 3 / s P r i n g - S u m m e r 1 9 7 4 ) , p. 5 5 -161 SELECTED BIBLIOGRAPHY Benjamin, W i l l i a m E. " P i t c h - C l a s s C o u n t e r p o i n t i n T o n a l M u s i c . " I n M u s i c Theory: S p e c i a l T o p i c s , pp. 1-32. E d i t e d by Richmond Browne. New York: Academic P r e s s I n c . , 1 9 8 1 . C l i f t o n , Thomas James. "Types o f a m b i g u i t y i n Schoenberg's t o n a l c o m p o s i t i o n s . " Ph.D. d i s s e r t a t i o n , S t a n f o r d U n i v e r s i t y , I966. Cone, Edward T. "Sound and S y n t a x : An I n t r o d u c t i o n t o Schoenberg's Harmony." P e r s p e c t i v e s o f New M u s i c ( F a l l - W i n t e r 197*0* 21-W. F r i e d h e i m , P h i l i p A l a n . " T o n a l i t y and s t r u c t u r e i n the e a r l y works o f Schoenberg." T h e s i s , New York U n i v e r s i t y , I 9 6 3 . L e w i n , D a v i d . "Toward t h e A n a l y s i s o f a Schoenberg Song (Opus 15 No. X I ) . " P e r s p e c t i v e s o f New Music ( F a l l - W i n t e r 1973/Spring-Summer 1974)* 4 3 - 8 6 . M a r t i n , Henry. "A S t r u c t u r a l Model f o r Schoenberg's Pe r v e r l o r e n e Haufen, Opus 1 2 / 2 . " I n Theory Only 3 TJune 1977 ) * 4-22 . Schoenberg, A r n o l d . Theory o f Harmony. T r a n s l a t e d by Roy E. C a r t e r . Los A n g e l e s : U n i v e r s i t y o f C a l i f o r n i a P r e s s , 1978 . Schoenberg, A r n o l d . S t r u c t u r a l F u n c t i o n s o f Harmony. New York: W. W. N o r t o n & Company, I n c . , 1954 ; r e v i s e d ed., e d i t e d by L e o n a r d S t e i n , New York: W. W. N o r t o n & Company, I n c . , I 9 6 9 . W i n t l e , W. "Schoenberg's harmony: t h e o r y and p r a c t i c e . " J o u r n a l o f the A r n o l d Schoenberg I n s t i t u t e 4 : 1 ( 1 9 8 0 ) : 5 0 -67 . 

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